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THE  MEASUREMENT 


OF 


INDUCTION    SHOCKS 

A    MANUAL    FOR    THE    QUANTITATIVE 
USE   OF   FARADIC    STIMULI 


BY 


ERNEST    G.    MARTIN,    Ph.D. 

ASSISTANT   PROFESSOR   OF   PHYSIOLOGY   IN   THE 
HARVARD   MEDICAL   SCHOOL 


FIRST  EDITION 

FIRST   THOUSAND 


NEW  YORK 

JOHN    WILEY    &    SONS 

London:  CHAPMAN   &   HALL,   Limited 

1912 


Copyright.  igi2, 

BY 

ERNEST  G.   MARTIN 


Stanbope  iptess 

.GILSON    COMPANY 
BOSTON,  U.S.A. 


PREFATORY    NOTE 


The  method  of  measuring  induction  shocks  described 
in  the  following  pages  was  developed  in  a  series  of  papers 
published  between  1908  and  191 1  in  the  American  Jour- 
nal -of  Physiology.  Extended  use  of  the  method  by 
myself  and  coworkers  has  shown  it  to  have  great  value 
in  many  physiological  and  psychological  researches.  In 
order  to  make  the  method  more  readily  available  for 
investigators,  and  with  the  hope  that  thereby  quantita- 
tive studies  may  be  more  generally  made,  the  scattered 
material  of  the  original  papers  has  been  assembled  into 
the  form  herein  presented.  Since  the  work  aims  to 
serve  rather  as  a  manual  than  as  an  exposition  of  prin- 
ciples, only  so  much  theoretical  matter  is  included  as  is 
necessary  to  make  inteUigible  the  procedures  adopted. 

E.  G.  M. 

Boston,  April,  19 12. 


CONTENTS 


CHAPTER  I. 

Page 

The  Characteristics  of  Induced  Currents i 

Introductory i 

Historical 2 

Structure  of  the  Inductorium 3 

Principle  of  the  Inductorium 4 

The  Form  of  Make  and  Break  Induced  Currents 8 


CHAPTER  II. 

Factors  which  Affect  the  Strengths  of  Far.adic  STiiiULi ....  12 

Sources  of  Variation 13 

Methods  Previously  Proposed 14 

Ptliiger 14 

Meyer-Fick 15 

Kronecker 16 

V.  Fleischl   18 

Wertheim-Salomonson 18 

Edclmann 20 

Hoorweg-Giltay 21 


CHAPTER   III. 

.\  Summary  of  Procedure 23 

Instruments  Required  for  the  Calibration 23 

Ammeter  and  Shunt 24 

Stimulating  Electrodes 27 

Procedure 28 

V 


VI  CONTENTS 

CHAPTER  IV. 

Page 
The  Physical  Principles  Underlying  the  Measurement  of 

Break  Shocks 32 

The  Course  of  Break  Induced  Currents 32 

CHAPTER  V. 

The  Determinations  of  Mutual  Induction  Between  Primary 

and  Secondary  Coils 38 

CHAPTER  VI. 
Effects  Produced  by  an  Iron  Core  in  the  Primary  Coil  ....       43 

CHAPTER  VII.  • 

Comparison  of  One  Coil  with  Another  —  The  Value  of  Z,  . . .       50 

CHAPTER  VIII. 
The  Preparation  of  a  Calibration  Scale  for  Break  Shocks  . .       55 

CHAPTER  IX. 

The  Make  and  Break  of  the  Primary  Circuit 60 

The  Knife-blade  Key 63 

The  Operating  Device 65 

The  Short-circuiting  Device 67 

CHAPTER  X. 

The  Influence  of  Secondary  Resistance  and  of  Cathode 

Surface 71 

The  Relation  of  Tissue  Resistance  to  Secondary  Resistance  as 

a  Whole 71 

Determination  of  Tissue  Resistance 72 

Effect  upon  the  Stimulus  of  Varying  the  Secondary  Resistance  73 

Current  Density,  an  Important  Factor .  .  .  .^ 76 


CONTENTS  vii 

CHAPTER  X  — Continued. 

Pace 
The  Dependence  of  Factor  A  upon  Inductorium  Construction       78 
Conditions  in  which  the  Specific  Stimulus  need  not  be  De- 
termined   '. 80 

A  Standard  of  Inductorium  Construction  Necessary 88 

CHAPTER  XI. 

The  Measurement  of  Make  Shocks 94 

Comparison  of  the  Gcineral  Formula?  for  Break  and  Make 

Stimuli 99 

CHAPTER  XII. 
Errors  to  be  Avoided 107 


INDUCTION   SHOCKS 


CHAPTER  I 
THE   CHARACTERISTICS   OF  INDUCED    CURRENTS 

Introductory.  The  inductorium  has  become  one  of 
the  most  famihar  and  most  useful  instruments  in  the 
physiological  laboratory.  There  are  few  physiological 
researches  which  do  not  involve  artificial  stimulation  of 
tissues;  and  for  the  production  of  stimuli  induction 
shocks  are  in  most  cases  the  first  choice.  They  are 
easier  to  use  and  they  subject  the  stimulated  tissue  to 
less  permanent  modification  than  do  other  forms  of 
artificial  stimulus.  Induction  shocks  are,  however,  very 
variable  in  intensity;  and  as  commonly  used  there  is 
no  means  of  knowing  or  of  stating  their  physiological 
effectiveness  in  other  than  the  most  general  terms.  An 
induction  shock  is  weak,  medium,  or  strong.  More 
closely  than  that  the  user  does  not  attempt  to  describe  it. 

This  lack  of  knowledge  as  to  the  strengths  of  the 
stimuli  employed  is  often  a  serious  handicap  in  the  pros- 
ecution of  individual  researches,  particularly  such  as 
call  for  the  use  of  stimuli  of  varying  strengths.     It  also 


2  INDUCTION  SHOCKS 

operates  to  make  uncertain  the  attempts  of  investigators 
to  duplicate  the  experiments  of  others. 

No  one  will  question  the  desirability  of  being  able  to 
measure  faradic  stimuli,  both  for  the  sake  of  controlling 
the  stimuli  used  in  one's  own  experiments,  and  also  in 
order  that  these  stimuli  may  be  so  described  as  to 
enable  other  workers  to  dupKcate  them  as  occasion 
arises. 

The  purpose  of  this  work  is  to  outline  a  system  for 
calibrating  the  apparatus  used  in  generating  induction 
shocks,  so  that  the  value  of  the  shocks  may  be  expressed 
in  terms  of  stimulation  units;  these  units  to  be  appli- 
cable to  any  properly  constructed  induction  apparatus, 
and  to  be  based  upon  determinations  which  can  be  made 
in  any  ordinarily  equipped  physiological  laboratory. 
The  system  proposed  is  not  a  new  departure,  but  is  an 
extension  and  amplification  of  previous  systems. 

Historical.  The  phenomenon  of  electromagnetic  in- 
duction was  discovered  by  Faraday  in  1831,  and  its 
physical  characteristics  were  very  thoroughly  worked 
out  by  him  and  by  Henry  about  the  same  time.  The 
first  suggestion  for  the  physiological  use  of  induction 
shocks  appears  to  have  been  made  by  Sturgeon*  in 
1837,  and  from  that  time  to  the  present  their  use  in  this 
connection  has  continued. 

Various  forms  of  induction  apparatus  have  been  de- 

*  Annales  de  Sturgeon:  1837,  p.  477. 


THE   CHARACTERISTICS   OF   INDUCED   CURRENTS      3 

vised,  but  for  physiological  purposes  only  one  has  come 
into  common  use;  this  form,  designed  by  E.  du  Bois- 
Reymond  *  in  1848,  is  illustrated  in  Figs,  i  and  2. 
Such  modifications  of  this  design  as  have  arisen  since 
its  introduction  have  to  do  only  with  details,  and  not  at 
all  with  the  underlying  principle  of  the  apparatus. 

Structure  of  the  Inductorium.     The  induction  coil,  as 
adapted  by  du  Bois-Reymond  to  physiological  use,  con- 


FlG.  I.  The  induction  coil  as  used  for  physiological  purposes 
(du  Bois-Reymond  pattern);  A,  the  primary  coil;  B,  the  secondary 
coil;  F',  binding  posts  to  which  are  attached  the  wires  from  the  battery 
—  they  connect  with  the  ends  of  coil  .4;  F",  binding  posts  connecting 
with  ends  of  coil  B,  through  which  the  induction  current  is  led  oil;  S, 
the  slide,  with  scale,  in  which  coil  B  is  moved  to  alter  its  distance  from  .4. 

sists,  in  essence,  of  two  coils  of  carefully  insulated  copper 

wire.     One  of  these,  the  primary  coil,  is  made  up  of 

two  or  three  layers  of  rather  coarse  wire  wound  upon  a 

hollow  core  of  nonconducting  material.      Usually  the 

outside  diameter  of  this  coil  is  about  2.5  to  4  cm.,  and 

its  length  between  8  and  14  cm.     The  number  of  turns 

*  du  Bois-Reymond:  Unters.  uber  tierische  Electrizitat,  1848,  Bd.  1, 
S.  447;  also,  Bd.  II,  I,  S.  393. 


4  INDUCTION  SHOCKS 

of  wire  does  not  ordinarily  exceed  600.  The  coil  is 
mounted  horizontally  by  one  end  upon  a  suitable  sup- 
port. The  ends  of  the  wire  are  brought  to  two 
binding  posts,  situated  at  some  convenient  place  on  the 
support. 

The  other  coil,  the  secondary,  consists  of  numerous 
turns  of  very  fine  insulated  wire,  wound  upon  a  hollow 
spool  whose  inside  diameter  is  such  that  the  secondary 
coil  can  be  brought  over  the  primary.  The  number  of 
turns  of  wire  is  usually  between  5000  and  10,000.  The 
length  of  the  secondary  coil  is  about  equal  to  that  of 
the  primary.  The  ends  of  the  wire  are  brought  to 
binding  posts  mounted  upon  the  spool.  A  sHde,  .30  or 
40  cm.  long,  projects  from  the  support  of  the  primary. 
The  secondary  is  mounted  upon  this  slide  with  its  axis 
coincident  with  the  axis  of  the  primary.  A  scale,  grad- 
uated in  millimeters,  is  mounted  on  the  slide.  A  pointer 
on  the  secondary  coil  is  so  placed  that  it  indicates  zero 
on  the  scale  when  the  secondary  covers  the  primary 
completely.  A  device  for  making  and  breaking  the 
primary  circuit  automatically  is  usually  included  as 
part  of  the  apparatus;  and  a  bundle  of  soft  iron  wire,  so 
constructed  as  to  sHde  into  the  hollow  core  of  the  pri- 
mary coil,  is  likewise  provided. 

Principle  of  the  Inductorium.  Whenever  a  steady 
current  is  flowing  through  the  primary  coil  there  exists 
about  it  a  magnetic  ''field  oj jorceP    This  field  may  be 


THE   CHARACTERISTICS   OF   INDUCED   CURRENTS      5 

pictured  as  consisting  of  "  lines  of  force  "  each  of  which 
passes  lengthwise  through  the  primary  coil,  and,  ex- 
tending a  greater  or  less  distance  from  it  into  space  at 
either  end,  curves  outward  and  back  so  that  the  two 
ends  meet,  making  each  "  line  of  force  "  a  closed  ellipse. 
The  lines  of  force  are  very  numerous  near  the  primary 
coil,  but  become  less  and  less  frequent  as  the  distance 
from  the  coil  increases.  The  number  of  lines  of  force 
present  and  the  distance  from  the  coil  at  which  they  can 
be  detected  depend  upon  the  intensity  of  the  current 
flowing  through  the  coil. 

If  another  coil  of  wire,  the  secondary,  be  placed 
within  the  field  of  force  about  the  primary  in  such 
position  that  lines  of  force  pass  lengthwise  through  it, 
any  alteration  in  the  number  of  lines  of  force  compre- 
hended within  the  secondary  generates  within  it  a  cur- 
rent which  is  the  induced  current.  This  current,  which 
depends  upon  changes  within  the  field  of  force,  ceases  to 
be  generated  whenever  the  field  of  force  becomes  steady, 
and  outlasts  the  change  in  the  field  only  the  brief  frac- 
tion of  a  second  required  for  the  current  to  die  away. 
The  direction  of  the  induced  current  depends  upon  the 
direction  of  the  current  through  the  primary  coil,  and  also 
upon  whether  the  change  in  the  field  is  an  increase  or  a 
decrease  in  the  number  of  lines  of  force.  The  iiitcnsity 
of  the  currents  induced  in  any  secondary  coil  depends 
upon  the  number  of  lines  of  force  moving  through  it, 


6  INDUCTION  SHOCKS 

and  also  upon  the  rate  of  their  movement;  the  more  rapid 
the  change  in  the  field,  the  higher  the  intensity. 

The  method  used  in  physiology  for  bringing  about 
alterations  of  the  field  within  the  secondary  coil  is  to 
make   and   break    the    current   through   the   primary. 


Fig.  2.  Schema  of  induction  apparatus  (Lombard),  h  repre- 
sents the  galvanic  battery  connected  by  wires  to  the  primary  coil  A. 
On  the  course  of  one  of  these  wires  is  a  key,  k,  to  make  and  break  the 
current.  B  shows  the  principle  of  the  secondary  coil  and  the  connec- 
tion of  its  two  ends  with  the  nerve  of  a  nerve-muscle  preparation. 
When  the  battery  current  is  closed  or  made  in  yl ,  a  brief  current  of  high 
intensity  is  induced  in  B.  This  is  known  as  the  making  or  closing 
shock.  When  the  battery  current  is  broken  m  A,  a,  second  brief  induc- 
tion current  is  aroused  in  B.  This  is  known  as  the  breaking  or  opening 
shock. 

When  the  primary  current  is  made  there  is  a  sudden  in- 
crease in  the  lines  of  force  cutting  the  secondary  coil; 
when  the  primary  current  is  broken  these  lines  of  force 
suddenly  disappear.  The  currents  induced  by  the  make 
and  the  break  of  the  primary  circuit  are  obviously  of 


THE   CIL\RACTERISTICS   OF   INDUCED   CURRENTS      7 

very  short  duration,  since  the  time  required  to  establish 
the  field  of  force  on  the  one  hand,  and  for  its  disappear- 
ance on  the  other,  is  measured  in  thousandths  of  a 
second,  and,  as  we  have  seen,  only  during  these  periods 
do  induced  currents  flow.  The  current  induced  in  the 
secondary  by  the  make  of  the  primary  circuit  is  usually 
spoken  of  in  physiology  as  the  make  shock;  that  induced 
by  the  break  of  the  primary  is  the  break  shock. 

A  feature  of  induction  shocks  which  commends  them 
particularly  to  the  physiologist  is  the  ease  with  which 
their  intensity  may  be  varied.  For  securing  this  varia- 
tion advantage  is  taken  of  the  dependence  of  the  induced 
current  upon  the  number  of  lines  of  force  which  cut  the 
secondary  coil.  There  are  two  ways  of  var>'ing  this 
number :  One  is  by  changing  the  intensity  of  the  primar>' 
current;  the  other,  by  shifting  the  position  of  the  sec- 
ondary coil  with  reference  to  the  primary.  This  latter 
method  is  the  one  used  in  the  du  Bois-Reymond  induc- 
torium,  and  it  is  a  very  satisfactory  method,  since  by 
means  of  it  the  strength  of  the  stimulus  can  be  varied 
several  hundredfold,  from  the  maximum  for  the  appa- 
ratus to  a  value  negligibly  small,  by  simple  shifting  of 
the  secondary  from  one  end  of  its  slide  to  the  other. 
Many  inductoria  are  so  constructed  that  the  secondary 
coil  can  be  rotated  about  an  axis  midway  of  its  length. 
In  this  way  the  intensity  of  the  induced  current  can  be 
cut  down  to  zero,  since  when  the  secondar>'  is  at  right 


8  INDUCTION  SHOCKS 

angles  to  the  primary  no  Knes  of  force  pass  lengthwise 
through  it.  For  quantitative  purposes,  however,  it  is 
better  to  have  a  rather  long  slide  and  to  keep  the  sec- 
ondary coil  always  with  its  axis  coincident  with  that  of 
the  primary. 

The  Form  of  Make  and  Break  Induced  Currents. 
When  a  circuit  is  closed  through  the  primary  coil  of  an 
inductorium  there  is  a  growth  of  the  current  within  this 
coil  from  zero  to  its  full  value.  Coincidently  with  this 
growth  of  current  there  is  being  established  a  field  of 
force  about  the  coil,  and  if  there  is  a  secondary  coil 
within  this  field  a  current  is  being  induced  therein. 
This  induced  current  also  begins  at  zero  and  increases 
in  intensity  during  the  establishment  of  the  field  of 
force  about  the  primary.  As  soon  as  the  field  is  fully 
established,  so  that  movement  of  the  lines  of  force 
ceases,  there  is  no  further  induction  and  the  current 
within  the  secondary  dies  away.  We  may  represent  the 
successive  changes  in  intensity  of  the  induced  current 
by  a  curve  such  as  that  shown  in  Fig.  3  in  which  the 
height  of  the  curve  at  any  point  represents  the  intensity 
of  the  induced  current  at  that  instant. 

The  rise  of  the  make  induced  current  from  zero  to  the 
maximum,  although  rapid,  is  by  no  means  instantaneous, 
there  being  a  well  marked  delay  in  the  establishment  of 
the  current  through  the  primary  coil  after  the  circuit  is 
closed.     This  delay  is  due  to  the  phenomenon  of  indue- 


THE   CHARACTERISTICS   OF   INDUCED    CURRENTS      9 

tance  within  the  primary  coil.  This  phenomenon  may  be 
explained  as  follows:  When  the  current  sweeps  through 
any  turn  of  wire  of  the  primary  coil  it  tends  to  establish 
a  held  of  force  about  that  turn;  but  as  the  lines  of  force 
composing  this  field  cut  through  adjacent  turns  of  wire 
of  the  primary  they  induce  currents  therein.  Since  en- 
ergy is  expended  in  this  inductance  the  currents  thus 
induced  cannot  be  in  the  same  direction  as  the  inducing 
current;  inasmuch  as  if  they  were,  there  would  be  a 


Fig.  3.  Curve  illustrating  the  growth  and  decline  of  a  make 
induced  current.  AB  represents  the  time  required  for  the  primary 
current  to  become  fully  established. 

gain  of  energy  —  a  thing  impossible ;  they  oppose  the  in- 
ducing current  and  allow  it  to  reach  its  full  value  only 
after  it  has  yielded  the  energy  necessary  for  the  induc- 
tance. In  Fig.  3  the  line  AB  represents  the  time  occu- 
pied by  the  primary  current  in  estabhshing  itself  against 
the  inductance,  and  therefore  the  time  during  which  the 
induced  current  increases. 

Any  condition  which  diminishes  the  inductance  within 
the  primary  coil,  thereby  allowing  the  primary  current 
to  establish  itself  more  quickly,  will  not  only  make  the 


lO  INDUCTION  SHOCKS 

ascending  limb  of  the  curve  of  Fig.  3  steeper,  but  will 
also  carry  it  higher;  that  is,  the  current  induced  in  the 
secondary  will  not  only  reach  its  maximum  intensity 
more  quickly,  but  that  maximum  will  be  greater;  this 
result  being  due  to  the  fact  that  the  intensity  is  greater 
the  more  rapid  is  the  alteration  in  the  field  of  force 
cutting  the  coil. 

While  a  current  is  flowing  steadily  through  the  pri- 
mary coil  no  induction  is  manifest ;  but  when  the  current 
is  broken  there  is  produced  in  the  secondary  coil  a 
break  induced  current.  The  agency  generating  this  cur- 
rent is  the  sudden  withdrawal  of  the  field  of  force  from 
the  secondary  coil. 

With  the  breaking  of  the  primary  circuit  it  would 
seem  at  first  thought  that  the  lines  of  force  should  dis- 
appear instantly  and  that  there  should  be  an  instan- 
taneous leap  of  the  break  induced  current  from  zero  to 
maximum.  As  a  matter  of  fact  the  growth  of  the  break 
current,  although  very  rapid,  is  not  instantaneous,  for  the 
reason  that  with  the  breaking  of  the  primary  circuit 
the  energy  absorbed  from  the  current  at  its  make  by 
the  inductance  within  the  coil  is  released  and  manifests 
itself  as  the  "  extra  current,"  jumping  across  the  points 
of  broken  contact  as  a  spark  and  prolonging  slightly 
the  decay  of  the  primary  current. 

The  chief  difference  between  Fig.  10,  p.  33,  which  rep- 
resents the  course  of  a  break  induced  current,  and  Fig.  3, 


THE   CHARACTKRISTICSOF   INDUCED    CURRENTS    II 

representing  a  make  current,  lies  in  the  greater  steep- 
ness of  the  ascending  limb  of  the  curve  of  the  break  cur- 
rent, due  to  the  shorter  period  occupied  by  the  spark 
in  passing.  Here  again  any  condition  that  hastens  the 
passage  of  the  spark  brings  about  increased  intensity 
of  induced  current  by  accelerating  the  disappearance  of 
the  field  of  force. 

Since  under  most  conditions  the  delay  in  establishing 
the  primary  current,  due  to  inductance,  is  greater  than 
the  delay  in  its  disappearance,  from  sparking  at  the  con- 
tacts, make  shocks  are  usually  less  intense  physiologi- 
cally than  are  break  shocks. 


CHAPTER  II 

FACTORS  WHICH  AFFECT  THE  STRENGTHS  OF  FARADIC 
STIMULI 

Any  scheme  for  measuring  induction  shocks,  if  it  is 
to  be  wholly  satisfactory,  must  take  into  account  all 
the  sources  of  possible  variation  present  in  the  mechan- 
isms by  which  the  shocks  are  generated  and  applied 
to  tissues.  The  numerous  methods  which  have  been 
worked  out  hitherto  have  been  uniformly  based  upon 
sound  physical  principles,  and  give  accurate  results  so 
far  as  they  go ;  they  leave  something  to  be  desired,  how- 
ever, in  that  none  of  them  deals  with  all  the  conditions 
of  variation  which  are  actually  present  whenever  tis- 
sues are  stimulated,  and  their  usefulness  is  limited  by 
just  that  much.  The  justification  for  the  present  work 
lies  in  its  attempt  to  take  into  account  all  the  sources 
of  variation  which  exist.  These  are  to  be  divided  into 
those  whose  influence  upon  the  strength  of  stimuH  is 
in  accordance  with  mathematical  laws,  determinable  by 
the  experimenter,  and  those  which  are  not  apparently  so 
determinable.  The  former  are  made  the  basis  for  the 
system  of  measuring  stimuli  herein  described;  the  latter 
are  studied  with  a  view  to  showing  how  their  effects 
may  be  minimized. 


STRENGTHS  OF  FARADIC   STIMULI  13 

Sources  of  Variation.  The  induction  apparatus,  as 
used  in  the  physiological  laboratory,  consists  of  two  cir- 
cuits: the  primary,  or  inducing  circuit,  which  includes 
the  primary'  coil  of  the  inductorium,  a  source  of  current, 
and  a  device  for  making  and  breaking  the  circuit,  to- 
gether with  the  necessary  connecting  wires;  and  the 
secondary  circuit,  including  the  secondary  coil,  wires 
leading  thence  to  suitable  stimulating  electrodes,  and 
the  tissue  to  be  stimulated.  In  Fig.  2,  p.  6,  these  cir- 
cuits are  illustrated  diagrammatically. 

In  any  given  primary  circuit  variations  may  arise 
either  in  the  amount  of  current  yielded  by  whatever 
source  of  current  is  used;  or  in  the  key,  whereby  the 
circuit  is  made  and  broken.  In  any  given  secondary 
circuit  variations  may  arise  in  the  position  of  the  sec- 
ondary coil  with  respect  to  the  primary,  this  being,  as 
we  have  seen,  the  usual  method  of  bringing  about  varia- 
tions in  stimulating  strength;  in  the  electrical  resistance 
of  the  tissue  which  is  being  stimulated;  and  in  the  con- 
tacts between  the  stimulating  electrodes  and  the  tissue 
to  which  they  are  appUed.  Also  different  inductoria 
usually  present  structural  differences,  such  as  different 
dimensions  and  dift'ercnt  numbers  of  turns  of  wire  in 
primary  and  secondary  coils,  which  themselves  bring 
about  wide  differences  in  the  strengths  of  stimuli  gen- 
erated by  the  different  inductoria.  The  presence  or 
absence  of  an  iron  core  within  the  primary  coil  is  also 


14  INDUCTION   SHOCKS 

a  source  of  great  modification  of  stimuli.  Finally,  as  we 
have  seen,  there  is  a  difference  in  physiological  effect 
between  make  shocks  and  break  shocks. 

Of  the  sources  of  variation  just  described  the  following 
are  subject  to  laws  which  are  determinable,  and  are  to 
be  included,  therefore,  in  our  quantitative  scheme:  The 
construction  of  the  inductorium,  the  position  of  the  sec- 
ondary coil  with  respect  to  the  primary,  the  presence  or 
absence  of  an  iron  core  in  the  primary,  the  intensity  and 
voltage  of  the  primary  current,  the  use  of  make  or  break 
shocks,  the  electrical  resistance  of  the  stimulated  tissue 
and  the  mode  of  contact  of  the  stimulating  electrodes 
with  the  tissue. 

The  variable  which  is  not  determinable  is  the  effect 
on  the  stimulus  of  the  manner  of  making  or  breaking 
the  primary  circuit.  This  must  be,  so  far  as  possible, 
made  uniform. 

Methods  Previously  Proposed.  The  first  attempt  to 
measure  induction  shocks  is  said  to  have  been  made  by 
Rosenthal  in  1857.*  Two  years  later  Pfliiger  made  quan- 
titative comparisons  between  shocks,  varying  their  in- 
tensities by  varying  the  primary  current,  leaving  all 
other  factors  constant.  His  method  gives  accurate  rela- 
tive results,  but  seems  not  to  have  commended  itself  to 
physiologists,  probably  because  it  calls  for  a  rather  com- 

*  See  Garten:  Handbuch  der  physiol.  Methodik,  1908,  Bd.  II, 
Abt.  3,  S.  393. 


STRENGTHS   OF    KARADIC   STIMULI  15 

plex   mechanism    for   varying  and   at   the    same    time 
measuring  the  primary  current. 

The  earliest  method  of  measuring  induction  shocks 
which  received  wide  recognition  was  worked  out  under 
the  direction  of  Fick  by  his  student,  Meyer,  in  1869.* 
This  method  concerned  itself  altogether  with  the  effect 
upon  the  intensity  of  break  shocks  of  shifting  the  posi- 
tion of  the  secondary  coil  relative  to  the  primary,  and 
amounts,  therefore,  to  a  calibration  of  the  slide  upon 
which  the  secondary  coil  moves.  By  such  calibration 
the  relative  intensities  of  the  shocks  given  by  the  in- 
ductorium  at  the  various  secondary  positions  are  accu- 
rately indicated,  so  long  as  all  the  other  variable  factors 
remain  unchanged.  A  similar  calibration  is  an  essential 
feature  of  any  scheme  for  the  quantitative  use  of  the 
inductorium,  and  indeed  the  only  criticism  of  the  Fick 
method  of  measuring  stimuli  is  for  its  incompleteness. 
The  Fick  calibration  was  accomplished  by  including  in 
the  secondary  circuit  a  galvanometer  and  determining 
the  current  induced  in  the  secondary  coil  at  its  various 
positions  by  the  deflection  produced  when  a  given  cur- 
rent was  made  or  broken  through  the  primary.  This 
method,  although  simple  in  theory,  was  in  fact  rather 
diflicult  to  put  into  practice  with  the  electrical  measuring 
apparatus  available   in   Fick's   time;    and   accordingly 

*  Meyer:  Unters.  phys.  Labor,  d.  Ziiricher  Hochschule,  Wien,  1869, 
S.  36. 


l6  INDUCTION  SHOCKS 

Kronecker,*  in  1871,  introduced  a  modification  of  the 
method  whereby  its  appHcation  was  simpHfied.  He  used 
two  inductoria,  connected  their  secondary  coils  in  series 
with  a  galvanometer  and  connected  both  primary  coils 
with  a  single  source  of  current  in  such  fashion  that  the 
two  secondaries  gave  induced  currents  opposite  in  direc- 
tion when  the  primary  circuit  was  broken.  Thus  the 
galvanometer  deflection  was  used  merely  as  an  indicator 
that  one  induced  current  was  stronger  than  the  other, 
rather  than  as  a  measure  of  the  strength  of  the  induced 
current  itself. 

With  both  secondaries  at  zero  the  primary  current 
was  broken  and  the  amount  and  direction  of  deflection 
noted.  The  coil  giving  a  stronger  shock  was  then  moved 
outward  till  no  deflection  occurred.  Then  the  weaker 
coil  was  moved  outward  till  a  deflection  equal  to  the 
first  one  was  obtained.  This  procedure  was  repeated 
till  the  whole  length  of  the  slide  had  been  traversed,  the 
number  of  times  the  stronger  secondary  was  moved  be- 
ing noted.  If  this  number  is  multiplied  by  the  original 
galvanometer  deflection  we  have  a  value  which  ex- 
presses how  many  times  greater  the  galvanometer  de- 
flection would  be  with  the  secondary  at  zero  than  at  the 
end  of  the  shde.  To  calibrate  the  slide  on  the  basis  of 
1000  units,  as  Kronecker  does,  the  total  deflection  noted 

*  Kronecker:  Arbeiten  aus  der  physiologischen  Anstalt  zu  Leipzig, 
1871,  S.  186. 


STRENGTHS  OF  FARADIC   STIMULI  17 

above  is  divided  by  1000  and  the  quotient  gives  the  gal- 
vanometer deflection  per  unit.  If  now  the  weaker  coil 
is  set  at  zero  and  the  stronger  at  a  point  such  that  the 
galvanometer  deflection  is  that  called  for  per  unit,  it  is 
possible,  by  repeating  the  original  procedure,  to  divide 
the  scale  into  1000  parts,  each  of  which  represents  a 
given  galvanometer  deflection,  and  therefore  an  equal 
decrement  in  stimulating  value.  This  method  has  the 
advantage  that  after  one  inductorium  is  calibrated  it  is 
extremely  easy  to  calibrate  others  to  correspond  with 
it,  by  connecting  the  calibrated  and  uncalibrated  coils 
in  the  manner  described  above  and  finding  the  corre- 
sponding points  on  the  two  slides.  Kronecker,  by  sub- 
stituting a  telephone  for  the  galvanometer,  made  the 
taking  of  readings  even  more  simple. 

The  method  has  the  disadvantage  that  it  is  purely 
arbitrary,  depending  at  the  outset  on  a  chance  difference 
of  stimulating  strength  occurring  in  two  inductoria; 
for  this  reason  the  calibration  can  only  be  duplicated 
through  access  to  a  coil  already  calibrated.  An  ob- 
ser\-er,  unable  for  any  reason  to  obtain  a  Kronecker  coil, 
might,  it  is  true,  prepare  a  caKbration  of  his  own  by 
repeating  Kronecker's  original  procedure,  but  he  could 
not  know  whether  his  units  represented  the  same  stimu- 
lating values  as  the  corresponding  Kronecker  units,  and 
so  could  not  express  satisfactorily  the  strengths  of 
stimuU  used  bv  him. 


1 8  INDUCTION  SHOCKS 

V.  Fleischl,*  in  1875,  proposed  a  method  of  calibrating 
the  inductorium  in  which  for  the  galvanometer  deflec- 
tion was   substituted   the   threshold   contraction   of   a 

I 

nerve-muscle  preparation.  In  this  calibration  the  de- 
creases in  stimulating  value  which  result  from  moving 
the  secondary  coil  outward  were  compensated  by  in- 
creasing the  current  through  the  primary  coil,  the  in- 
creases required  being  taken  as  the  measure  of  the 
change  in  stimulating  intensity  resulting  from  the  move- 
ment of  the  secondary.  This  method  has  the  advantage 
of  being  available  in  situations  where  no  galvanometer 
can  be  obtained.  Its  greatest  importance  lies,  however, 
in  confirming  the  assumption  of  Fick  and  of  Kronecker 
that  the  physiological  intensities  of  break  induced  cur- 
rents are  proportional  to  the  galvanometer  deflections 
they  produce. 

Wertheim-Salomonsonf  has  recently  described  a 
method  for  obtaining  a  physiological  calibration  in 
which  variations  in  the  primary  current  are  avoided. 
He  places  the  nerve  of  the  nerve-muscle  preparation  to 
be  used  as  an  indicator  in  one  branch  of  a  divided  sec- 
ondary circuit,  and  in  the  other  branch  places  a  re- 
sistance equal  to  that  of  the  nerve.  (See  Fig.  4.)  The 
resistance  of  the  divided  circuit  is  then  one-half  that  of 

*  V.  Fleischl:  Sitzb.  d.  k.  Akad.  d.  Wissensch.  Wien,  1875,  Bd. 
Ixxii,  Abth.  III.     Also  Ges.  Abh.,  1893,  S.  475. 

t  Wertheim-Salomonson:  Zeitschr.  f.  Elektrother.  I.,  1899,  S.  97. 


STRENGTHS  OF  FARADIC   STIMULI  19 

the  nerve  alone.  By  placing  in  the  circuit  beyond  the 
shunt  another  resistance  equal  to  one-half  that  of  the 
nerve  the  total  resistance  of  the  secondary  circuit  is 
made  equal  to  what  it  would  be  if  the  shunt  and  the 
added  resistance  were  both  removed.  Since,  however, 
the  nerve  is  in  a  divided  circuit,  both  branches  of  which 
huve  equal  resistance,  it  receives  only  one-half  the  cur- 
rent generated  in  the  secondary  coil.  That  secondary 
position  at  which  the  nerve  receives  threshold  stimula- 
tion when  in  the  divided  circuit  is  determined,  and  then 

Nerv-e,  of  Res.  W 


W 
Fig.  4.     Diagram  showing  method  of  inserting  resistances  in  the 
Wertheim-Salomonson  method  of  calibration.     After  Gasten. 

the  shunt  and  the  additional  resistance  are  cut  out. 
Now  the  nerve  receives  the  whole  current  from  the  sec- 
ondary instead  of  half  of  it,  and  if  the  secondary  posi- 
tion is  found  at  which  the  threshold  stimulus  is  again 
imparted  we  know  that  this  second  current  has  just 
half  the  stimulating  value  of  the  first.  We  have  thus  a 
method  for  comparing  stimuli,  which  admits  of  exten- 
sion sufficient  for  the  complete  calibration  of  a  coil. 
It  has,  however,  the  shortcoming,  already  noted  for 
Kronecker's  method,  of  giving  values  applicable  only 


20  INDUCTION  SHOCKS 

to  the  single  coil  on  which  it  is  worked  out.  One  very 
important  feature  of  a  wholly  satisfactory  calibration 
must  be  its  general  applicability,  so  that  any  properly 
constructed  inductorium  can  be  calibrated^  in  any  labo- 
ratory to  give  results  comparable  with  those  obtained 
from  other  calibrated  instruments. 

Moreover,  it  is  not  to  be  forgotten  that  no  method 
of  calibration  thus  far  described  takes  into  account  the 
effects  of  strength  of  primary  current,  of  tissue  resistance, 
or  the  method  of  applying  the  stimulating  electrodes, 
all  of  which  are  important,  and  at  the  same  time  de- 
terminable, and  therefore  to  be  included  in  a  complete 
calibration  scheme;  nor  do  any  of  them  consider  the 
strength  of  make  shocks,  all  being  available  only  for 
breaks. 

A  device  which  is  superior  in  certain  respects  to  any 
thus  far  described  for  measuring  stimuli  is  the  "  fara- 
dimeter  "  of  Edelmann.  In  this  apparatus  a  galvanom- 
eter in  the  secondary  circuit  registers  the  voltage  of  the 
induced  current.  The  galvanometer  readings  give  cor- 
rect indications  of  the  values  of  stimuli  only  when  a 
current  of  definite,  fixed  amperage  is  broken  in  the 
primary  circuit.  It  is  necessary,  therefore,  to  have  a 
source  of  currents  specially  selected  to  give  this  amper- 
age, and  by  means  of  an  ammeter  in  the  primary  cir- 
cuit to  insure  that  it  is  maintained.  The  Edelmann 
method  is  an  advance  over  others  in  that  it  takes 


STRENGTHS   OF   lAR/VDIC   STIMULI  21 

account  of  the  factor  of  primary  current  strength  and 
provides  for  its  regulation.  It  docs  not,  however,  take 
account  of  the  influence  upon  the  strength  of  stimulus 
of  variations  in  tissue  resistance,  since  the  quantity 
measured  by  the  galvanometer,  namely  the  \oltage,  is 
independent  of  the  resistance.  Nor  does  it  consider  the 
effect  of  the  method  of  application  of  the  stimulating 
electrodes.  But  so  long  as  these  two  factors  remain 
constant  the  Edelmann  faradimeter  gives  accurate  re- 
sults for  break  shocks,  and  expresses  them  in  terms 
such  that  the  stimuli  used  by  one  worker  can,  save  for 
the  factors  above  mentioned,  be  duplicated  by  others. 
The  importance  of  taking  secondary  resistance  into 
account  was  brought  out  by  Hoorweg*  in  1893.  He 
demonstrated  the  effect  of  variations  in  resistance  in 
modifying  stimulation  strengths,  and  emphasized  the 
necessity  of  working  out  some  method  by  which  to 
ascertain  this  effect.  At  his  suggestion  Giltay  y  de- 
signed an  electrodynamometer  by  which  the  variations 
in  strength  of  stimulus  due  to  varying  secondary  re- 
sistances can  be  read  directly.  This  apparatus  fulfils 
admirably  the  purpose  for  which  it  was  designed.  It 
is,  however,  of  little  practical  use  in  physiology',  since 
its  readings,  to  be  comparable,  must  be  made  with  the 

*  Hoorweg:  Die  mediclnische  Elektrotechnik  und  ihre  phj'sikalischen 
Grundlagen,  Leipzig,  1893. 

t  Giltay:  Annalen  der  Physik  und  Chemie,  1893,  Bd.  50,  S.  756. 


22  INDUCTION   SHOCKS 

same  inductorium  or  with  inductoria  of  piecisely  similar 
construction,  and  the  position  of  the  secondary  coil 
with  respect  to  the  primary  must  not  be  altered.  In 
view  of  the  fact  that  moving  the  secondary  coil  is  the 
usual  method  among  physiologists  for  varying  the 
strength  of  stimulus,  this  instrument  clearly  does  not 
altogether  meet  the  requirements  of  physiological  work. 
It  has,  moreover,  the  somewhat  serious  shortcoming 
of  taking  no  account  of  the  method  of  applying  the 
stimulating  electrodes,  so  that,  even  were  all  the  other 
conditions  met,  the  electrodynamometer  would  still  fail 
to  give  wholly  complete  measurements. 

Our  examination  of  the  various  systems  hitherto  pro- 
posed for  measuring  induction  shocks  bears  out  the 
statement  made  at  the  outset  that  none  of  them  meets 
fully  the  requirements  of  quantitative  work.  We  are 
justified  therefore  in  submitting  a  system  which,  although 
not  new,  being  an  extension  of  the  Fick-Kronecker 
method,  attempts  to  deal  with  all  the  factors  concerned 
in  the  production  of  faradic  stimuli,  so  that  henceforth 
the  values  of  stimuli  may  be  expressed  in  such  terms 
that  they  can  be  duphcated  or  modified  quantitatively 
at  will. 


CHAPTER   III 
A   SUMMARY   OF  PROCEDURE 

For  the  convenience  of  users  of  the  method  herein 
presented  it  has  been  thought  worth  while  to  describe 
briefly  at  the  outset  the  various  pieces  of  apparatus 
used  and  to  summarize  the  various  procedures  involved 
in  making  the  necessary  calibrations  and  in  using  the 
calibrated  apparatus. 

Instruments  Required  for  the  Calibration.  The  in- 
ductorium  to  be  calibrated  should  be  of  "  standard  " 
construction  (sec  p.  88),  that  is,  it  should  have  a  sec- 
ondary coil  approximately  13  cm.  long  and  having  about 
10,000  turns  of  wire.  The  number  of  turns  and  the 
mean  cross  section  of  the  secondary  coil  must  be  accu- 
rately known  (p.  55).  The  shde  upon  which  the  sec- 
ondary moves  should  be  not  less  than  30  cm.  long.  It 
should  be  accurately  graduated  in  millimeters,  and  a 
pointer  fixed  to  the  secondary  coil  in  such  position  as  to 
stand  at  zero  when  the  secondary  is  pushed  completely 
over  the  primary.  To  increase  the  stimulating  effec- 
tiveness of  the  instrument  the  primary  coil  should  have 
a  core  made  of  a  bundle  of  soft  iron  wires. 

In  addition  to  this  inductorium  there  is  needed  a  con- 

23 


24 


INDUCTION  SHOCKS 


stant  source  of  current  sufficient  in  amount  to  yield  at 
least  I  ampere  through  the  resistance  of  the  primary- 
coil.  Where  a  charging  current  is  available,  probably  a 
good  storage  battery  will  be  found  most  convenient  as  a 
source  of  current.  Several  Daniell  cells  in  series,  how- 
ever, answer  every  pur- 
pose. A  good  ammeter 
for  measuring  the  inten- 
sity of  the  primary  current 
is  required,  as  is  also  a 
variable  resistance  for  ad- 
justing its  amount.  Since 
it  is  often  necessary  in 
the  course  of  the  work 
to  use  currents  ranging 
from  o.oooi  ampere  to  i 
ampere  the  ammeter  must 
be  able  to  cover  this  range. 
No  instrument  is,  of 
course,   able   to  measure 

Fig.  5.  Diagram  showing  ammeter  the  small  Currents  with 
sh^nt  made  from  a  Porter  metal-  g^^^ient  accuracy  and 
contact  rockmg  key.  _         -^ 

at  the  same  time  to  give 
direct  readings  for  the  larger  ones.  To  give  the 
ammeter  the  desired  range,  therefore,  recourse  must  be 
had  to  a  system  of  shunts.  I  have  found  it  convenient  to 
use  a  milammeter  having  a  scale  capacity  of  10  mil  am- 


A  SUMMARY  OF  PROCEDURE  25 

peres  and  reading  directly  to  o.i  mil  ampere,  and  to 
provide  it  with  two  shunts,  one  adjusted  to  carry  nine- 
tenths  of  the  total  current,  the  other  to  carry  ninety- 
nine  one-hundredths  of  the  current.  For  these  shunts 
I  use  an  ordinary  Porter  metal-contact  rocking  key 
connected  as  shown  in  the  diagram.  Fig.  5.  For  the 
YU  shunt,  German  silver  wire  is  used  between  one 
pair  of  end  contacts;  for  the  jo%  shunt,  copper  wire  is 
used  between  the  other  pair  of  end  contacts.  To  cali- 
brate the  shunts,  resistance  is  introduced  into  the  am- 
meter circuit  until  exactly  o.oi  ampere  is  flowing;  then 
the  shunts  are  adjusted  until  the  ammeter  reading  is 
exactly  o.ooi  ampere,  when  the  iq  shunt  is  in  circuit, 
and  o.oooi  ampere  when  the  iVo  shunt  is  in.  The 
shunts  must  be  recalibrated  at  frequent  intervals,  but 
this  is  not  a  difficult  task. 

As  a  means  of  adjusting  the  amount  of  primary  cur- 
rent flowing  I  have  found  a  dial  resistance  box  most 
satisfactory,  although  any  available  variable  resistance 
can  be  used.  The  total  resistance  should  not  be  less 
than  11,000  or  12,000  ohms,  since  with  a  source  of  cur- 
rent yielding  2  volts  that  amount  of  resistance  is  often 
necessary-  to  cut  the  current  down  to  the  point  where 
threshold  stimuli  are  produced. 

For  making  and  breaking  the  primary  circuit  some 
form  of  automatic  key  is  required.  A  satisfactory'  one 
is  described  in  Chapter  IX.    Experience  shows  that  trust- 


26  INDUCTION  SHOCKS 

worthy  results  cannot  be  obtained  with  a  key  which 
fails  to  give  uniform  breaks.  Uniform  makes  are  very 
desirable,  but  for  many  sorts  of  work,  including  the 
routine  of  making  the  calibration,  make  shocks  need  not 
be  employed. 

All  the  apparatus  thus  far  described  is  required  for 
the  quantitative  use  of  the  induction  coil  as  well  as  for 
its  calibration.  Additional  instruments  needed  for  mak- 
ing the  calibration  are  a  good  ballistic  galvanometer  and 
a  standard  induction  apparatus.  A  satisfactory  form 
of  ballistic  galvanometer  is  the  d'Arsonval  wall  instru- 
ment with  moving  coil  and  reflected  scale,  read  with  a 
telescope.  The  standard  induction  apparatus  can  be 
made  in  any  machine  shop.  It  consists  of  a  primary 
coil,  at  least  75  cm.  long  and  composed  of  a  single  layer 
of  heavy  insulated  wire,  carefully  wound,  and  a  sec- 
ondary coil,  not  over  15  cm.  long,  of  about  2000  turns 
of  fine  wire,  placed  exactly  at  the  center  of  the  primary 
coil.  The  cross  section  and  number  of  turns  per  centi- 
meter of  the  primary  coil  must  be  known,  and  the  total 
number  of  turns  of  the  secondary. 

Additional  apparatus  required  in  the  use  of  the  in- 
ductorium,  but  not  in  the  calibration,  is,  first,  a  device 
for  determining  tissue  resistance,  and,  second,  suitable 
stimulating  electrodes.  I  have  found  the  Kohlrausch 
method  of  measuring  resistance  perfectly  satisfactory 
(see  p.  72).     This  method  requires  an  ordinary  meter 


A  SUMMARY   OF  PROCEDURE  27 

bridge,  a  small  inductorium  to  give  an  alternating  cur- 
rent, a  telephone  receiver  for  an  indicator  and  a  resist- 
ance box.  By  suitable  wiring,  illustrated  in  Fig.  15, 
p.  73,  a  single  resistance  box  can  be  used  both  for  vary- 
ing the  primary  current  and  as  the  known  resistance  in 
the  Kohlrausch  determinations. 

The  stimulating  electrodes  must  be  selected  with 
special  reference  to  uniformity  of  contact.  Accurate 
quantitative  results  cannot  be  gotten  under  conditions 
of  contact  variation.  For  the  direct  stimulation  of 
muscles  I  have  found  platinum  needle  electrodes  most 
satisfactory.  A  piece  of  platinum  wire  2.5  to  3  cm. 
long,  and  0.5  mm.  in  diameter,  pointed  somewhat  at  the 
end  with  a  file,  is  soldered  to  a  suitable  length  of  very 
fine  copper  wire  (diameter  0.2  mm.).  The  platinum 
needle  is  thrust  directly  into  or  through  the  muscle 
tissue;  the  copper  wire,  carried  to  the  secondary  ter- 
minal, affords  the  very  flexible  connection  necessary  for 
avoiding  interference  with  the  free  movement  of  the 
muscle. 

For  stimulating  nerves  the  glass-inclosed  electrodes 
described  by  Sherrington  *  are  as  reliable  as  any  I  know 
of.  They  answer  well  either  for  the  stimulation  of  nerves 
deeply  imbedded  within  the  body,  or  for  stimulating  the 
nerve  of  the  ordinary  nerve-muscle  preparation.  In  the 
use  of  this  form  of  electrode  care  must  be  taken  that  the 

*  Sherrington:  Jour,  of  Physiol.,  1909,  x.xxviii,  p.  382. 


28  INDUCTION  SHOCKS 

interior  of  the  glass  tube  is  clear  of  liquid.  The  elec- 
trode is  shown  in  Fig.  6;  contact  is  made  by  rotating 
slightly  the  stopper  carrying  the  two  platinum  wires. 

For  the  determination  of  "  specific  "  stimulation  val- 
ues (see  p.  76),  a  rather  large  known  resistance,  ten 
thousand  to  twenty  thousand  ohms,  must  be  arranged  to 
be  included  in  the  secondary  circuit  as  required. 


Fig.  6.     Shielded  electrodes  (Sherrington). 

The  arrangement  of  apparatus  for  making  the  cali- 
bration is  illustrated  diagrammatically  in  Fig.  7.  The 
procedure  is  by  the  following  steps,  for  each  of  which 
a  page  reference  is  given. 

1.  Determination  of  the  formula  for  core  magnetiza- 
tion (p.  43). 

2.  Determination  of  the  mutual  induction  for  a  series 
of  selected  secondary  positions  from  12  cm.  outward 
(P-  38). 


A   SUMMARY    OK    PROCKUURE 


29 


m 


Fig.  7.  Arran<,'cmcnt  of  apparatus  for  calibrating  the  inducto- 
rium.  .1,  ammeter;  B,  l)atlcry;  C,  standard  coil;  G,  galvanometer; 
/,  induclorium  to  be  calibrated;  A',  make  and  break  key;  P,  apparatus 
for  physiological  calibration;   R,  resistance  box;  5  and  Si,  switches. 


3.  Determination  of  the  inductance  of  the  secondary 
coil  (p.  50). 

4.  Determination  of     -  for  the  secondary  positions 

whose  mutual  inductions  have  been  estabHshed  (p.  53). 

5.  Physiological  corroboration  of  this  calibration  by 
the  V.  Fleischl  method  (p.  56),  accompanied  by  physi- 
ological determination  of  the  "  cahl)ration  numl)ers  "  for 
the  inner  secondary  positions  (p.  58). 

6.  Construction  of  a  curve  to  establish  calibration 
numbers  for  intermediate  secondary  positions  (p.  56). 

7.  Determination  of  the  constant  C  in  the  formula  for 
make  shocks  (\)\).  94  and  104). 


30 


INDUCTION   SHOCKS 


Fig.  8.  Arrangement  of  apparatus  for  the  use  of  the  quantitative 
method,  i,  battery;  2,  resistance  box  in  primary  circuit;  3,  slide 
wire  resistance  for  fine  adjustment;  4,  ammeter;  5,  ammeter  shunt; 
6,  make  and  break  key  with  automatic  short-circuiting  device  for  make 
or  break  shocks;  7,  inductorium;  8,  resistance  box  in  secondary  circuit; 
9,  wires  leading  to  stimulating  electrodes. 


zsmBmxms&i^i 


Fig.  9.    View  of  apparatus  in  actual  use.     Significance  of  numbers 
is  the  same  as  in  Fig.  8. 


A  SUMMARY   OF   PROCEDURE  31 

The  arrangement  of  apparatus  for  the  use  of  the 
quantitative  method  is  indicated  diagrammatically  in 
Fig.  8.  The  diagram  is  self-explanatory.  As  an  addi- 
tional guide,  a  photograph  of  a  set  of  apparatus  in  actual 
use  is  reproduced  in  Fig.  9.  In  the  final  chapter  of  the 
book  various  precautions  are  described  which  much  ex- 
perience with  the  method  has  suggested. 


CHAPTER  IV 

THE  PHYSICAL  PRINCIPLES  UNDERLYING  THE  MEASURE- 
MENT  OF  BREAK   SHOCKS 

Helmholtz*  appears  to  have  been  the  first  to  study 
in  detail  break  induction  shocks.  He  established  the 
principles  which  are  still  accepted  as  to  their  formation 
and  course.  His  work  was  chiefly  from  the  physical 
standpoint,  although  he  gave  attention  also  to  the  physi- 
ological aspect  of  the  problem.  More  recently  Fleming  f 
has  given  a  clear  and  concise  discussion  of  break  induc- 
tion shocks,  his  presentation  agreeing  in  every  essential 
particular  with  the  earlier  one  of  Helmholtz.  The  fol- 
lowing statement  is,  in  the  main,  condensed  from  Flem- 
ing's discussion. 

The  Course  of  Break  Induced  Currents.  The  current 
induced  in  a  secondary  coil  by  the  breaking  of  the 
primary  current  may  be  represented  graphically  by  such 
a  curve  as  is  given  in  Fig.  lo,  beginning  at  zero,  increas- 
ing rapidly  to  a  maximum,  and  then  falHng  more  slowly 
away  to  zero.     If  the  break  of  the  primary  were  abso- 

*  Helmholtz:  Poggendorf's  Annalen  der  Physik  und  Chemie,  1851, 
Ixxxiii,  S.  536.     Also,  Ges.  Abh.,  S.  459. 

t  Fleming:  The  Alternate  Current  Transformer,  London,  1892,  i, 
pp.  184  et  seq. 

32 


THE  MEASUREMENT  OF  BREAK  SHOCKS 


33 


A 

Fig.  io.     Curve  illustrating  the  course 

of  a  break   induced   current  —  after 

Fleming. 


lutely  instantaneous,  the  initial  rise  would  be  instan- 
taneous likewise  and  the  secondary  current  would  begin 
with  its  maximum  value.  Since,  however,  there  is  al- 
ways, even  under  most  favorable  conditions,  a  certain 
amount  of  sparking  at 
the  contacts,  there  is 
never  an  instantaneous 
break,  and  the  initial 
rise  is  constantly 
present.  Helmholtz  * 
demonstrated,  with  the 
aid  of  an  ingenious  ap- 
paratus, that  the  phys- 
iological effect  of  a  break  induced  current  is  chiefly 
exerted  by  that  part  embraced  within  the  ascending  limb 
of  the  curve.  By  breaking  the  secondary  current  at 
various  points  in  its  course  he  found  that  the  physiolog- 
ical effect  was  virtually  as  great  when  the  current  was 
broken  at  the  moment  of  reaching  its  maximum  intensity 
as  when  it  was  allowed  to  run  its  entire  course.  Recent 
investigations  carried  out  by  means  of  short  galvanic 
currents  have  shown,  it  is  true,  that  the  stimulating 
effectiveness  of  a  shock  is  to  some  extent  dependent  as 
well  upon  the  descending  portion  of  the  curve,!  so  that 

*  Helmholtz:  Loc.  cit.,  S.  537. 

t  Gildemeister:     Pfluger's   Archiv    fur    die   gesammte    Physiologic, 
cxxxi,  1910,  S.  199. 


34  INDUCTION  SHOCKS 

Helmholtz'  conclusion  is  not  wholly  valid.  But  at  this 
stage  of  the  discussion  we  may  neglect  the  effect  of  the 
descending  portion  of  the  curve,  and  proceed  as  though 
the  ascending  Umb  were  the  sole  determining  factor. 

Since  the  chief  physiological  effect  is  exerted  during 
the  growth  of  the  current  this  effect  will  be  greater  the 
higher  the  curve  rises;  in  other  words,  the  strength  of 
stimulus  tends  to  be  proportional  to  the  maximum  in- 
tensity of  the  induced  current.  In  the  diagram,  Fig.  lo, 
the  maximum  intensity  is  represented  by  the  ordinate 
CB,  drawn  from  the  base  line  to  the  summit  of  the  curve, 
and  with  the  factors  determining  the  value  of  this  ordi- 
nate we  are  at  present  concerned. 

Helmholtz  showed  that  the  induced  current  reaches 
its  maximum  intensity  at  the  instant  the  spark  ceases  to 
pass.  The  abscissa  AB,  therefore,  represents  the  time 
occupied  by  the  spark.  In  a  properly  constructed  ap- 
paratus AB  will  be  constant.  Helmholtz  showed  also 
that  the  value   of   the  ordinate   CB  is  approximately 

MI    .  .  . 

equal  to  -p-'  in  which  M  is  the  mutual  induction  be- 

tween  primary  and  secondary,  I  the  intensity  of  the  cur- 
rent through  the  primary,  and  L  the  inductance  of  the 
secondary.  If  the  break  were  instantaneous,  making 
AB  zero,  CB  would  equal  the  expression  given  above; 
it  falls  below  that  value  more  and  more  as  AB  increases, 
but  so  long  as  ^5  is  constant  the  relation  between  the 


THE  MEASUREMENT  OF  BREAK  SHOCKS     35 

MI  .        . 

true  value  of  CB  and  the  value  — -'  which  it  approxi- 

mates,  docs  not  vary. 

MI 

We  may  use  the  expression  — — '  therefore,  as  a  physi- 
cal basis  for  the  measurement  of  break  shocks,  although 
we  must  note  that  the  expression  will  not  serve  fully, 
since  the  factor  of  secondary  resistance  is  not  included 
in  it,  nor  is  there  any  factor  for  the  influence  of  the 
manner  of  applying  the  stimulating  electrodes.  More- 
over, the  expression  is  proportional  to  the  strength  of 
the  stimulus  only  so  long  as  the  circuit  is  broken  uni- 
formly. The  expression  serves  in  our  quantitative 
scheme,  therefore,  only  as  a  starting  point.  Its  use  even 
so  far  is  justifiable  only  if  physiological  tests  confirm  the 
applicability  of  the  physical  relationships.  That  they 
do  so  completely  will  be  shown  in  due  course. 

Our  next  step  is  a  consideration  of  the  indi\'idual 

factors  m  the  expression  — —  and  a  discussion  of  the 

means  whereby  they  are  to  be  determined. 

Of  the  three  factors  which  make  up  the  expression, 
one,  /,  the  intensity  of  the  primary  current,  is  an  easily 
measured  electrical  quantity,  and  is  best  determined 
directly  by  means  of  an  ammeter  in  the  primary  circuit. 
The  other  two,  M  and  L,  are  functions  of  the  construc- 
tion of  the  inductorium,  either  by  itself  or  as  modified 


36  INDUCTION  SHOCKS 

by  the  relative  positions  of  the  primary  and  secondary 
coils.  M,  the  mutual  induction  between  the  primary 
and  secondary  coils,  varies  with  changes  in  the  position 
of  the  secondary  relative  to  the  primary,  but  is  fixed  for 
each  position.  It  can  therefore  be  determined  once  for 
each  position  of  the  secondary  coil,  and  the  values  thus 
obtained  used  in  all  future  calculations. 

Since  mutual  induction  is  the  factor  which  varies 
with  shifts  in  the  position  of  the  secondary  coil  relative 
to  the  primary,  most  of  the  calibrations  hitherto  pro- 
posed amount  in  effect  to  determinations  of  the  relative 
mutual  inductions  for  the  various  secondary  positions. 
That  the  stimulating  power  should  theoretically  be  pro- 
portional to  the  mutual  induction  so  long  as  the  other 
factors  remain  constant  is  obvious  from  inspection  of  the 

MI  rr,^  ^  •  1,  ,  • 

expression  — —  •     That  the  proportion  really  does  exist 

is  ^proved  by  the  experimental  verification  of  the  Fick, 
Kronecker,  and  Edelmann  calibrations,  as  well  as  by  the 
experiments  carried  out  in  the  development  of  the  pres- 
ent method.* 

L,  the  inductance  of  the  secondary  coil,  is  a  function 
of  the  construction  of  the  coil  and  is  therefore  constant 
for  any  given  inductorium  except  as  it  is  modified  by 
extraneous  influences.     When  the  inductorium  is  used 

*  Martin:  Amer.  Jour,  of  Physiol.,  1908,  xxii,  p.  123. 


THE  MEASUREMENT  OF  BREAK  SHOCKS     37 

with  an  iron  core  in  the  primary,  this  acts  to  modify  the 
value  of  L  whenever  the  secondary  coil  is  directly  over 
the  iron  core. 

The  methods  by  which  M  and  L  are  determined  in 
practice  are  outhned  in  succeeding  chapters. 


CHAPTER  V 

THE  DETERMINATIONS   OF  MUTUAL  INDUCTION 
BETWEEN  PRIMARY  AND   SECONDARY   COILS 

In  determining  the  mutual  induction  for  the  various 

secondary  positions  advantage  is  taken  of  the  fact  that 

this  factor  appears  in  the  expression  for  the  integral 

effect  of  the  induced  current.     This  integral  effect  is 

represented  in  the  diagram  (Fig.  lo),  by  the  entire  area 

.    MI    . 
ABCD;  its  expression  is  — —  >  in  which  M  and  /  have 

the  same  meanings  as  hitherto,  and  R  equals  the  resist- 
ance in  the  secondary  circuit.  The  integral  effect  can 
be  measured  by  means  of  the  ballistic  galvanometer. 
For  this  purpose  the  secondary  of  the  induction  coil 
under  examination  is  connected  in  series  with  a  good 
ballistic  galvanometer  and  with  the  secondary  of  a 
standard  induction  coil,  the  latter  apparatus  being  so 
constructed  that  the  mutual  induction  between  its  pri- 
mary and  secondary  coils  can  be  computed  from  the  con- 
struction of  the  apparatus  and  the  current  through  the 
primary.  The  special  features  of  its  construction  are 
found  in  the  primary,  which  is  a  solenoid  of  one-layer 
thickness,  very  evenly  wound,  and  several  times  longer 

38 


PR1.M.\K\     AM)    SFX'OXDARY    COILS  39 

than  the  secondary.  The  lines  of  force  through  the 
secondary,  placed  at  the  middle  of  the  primary,  are  then 
practically  straight.  The  arrangement  of  the  apparatus 
is  shown  diagrammalically  in  Fig.  7. 

The  secondary  of  the  inductorium  whose  values  of 
M  are  desired  is  set  successively  at  points  i  or  2  cm. 
apart.  At  each  point  the  galvanometer  deflection 
caused  by  breaking  a  primary  current  of  known  inten- 
sity is  determined.  Since  each  galvanometer  deflec- 
tion represents  a  certain  integral  efTect,  no  matter  how 
produced,  and  since  the  integral  effect  afi'ords  means 
of  computing  M,  a  determination  of  the  intensity  of  cur- 
rent which  has  to  be  broken  in  the  primary  of  the 
standard  coil  to  produce  these  same  deflections  provides 
all  the  data  required  for  calculating  the  values  sought. 
The  formula  used  for  computing  M  is  developed  in  the 
following  manner:   The  expression  for  the  integral  effect 

is,  as  stated  above,  -  ~-  •      Let  this  represent  the  gal- 
K 

vanometer  deflection  caused  by  breaking  a  current  of 

intensity  /  in  the  primary  of  the  coil  whose  values  of  ^[ 

are  desired.     Let  the  expression  --  -^  represent  the  same 

R 

galvanometer  deflection  caused  by  breaking  a  current  of 

intensity  S  through  the  primary  of  the  standard  coil. 

MI      M'S 

Equating  these,  we  have——  =  — — -•      The  method  of 

K  K 


40  INDUCTION  SHOCKS 

connecting  the  secondaries  is,  as  stated  previously,  pur- 
posely such  that  the  value  of  R  is  constant  throughout. 
It  therefore  disappears  from  the  equation  and  we  have 
MI  =  M'S.  The  value  of  M'  is  computed  from  the 
construction  of  the  standard  coil  according  to  the  formula 
M'  =  4  TTfiNAS,  in  which  n  equals  the  number  of  turns  in 
the  primary  coil  per  centimeter  of  length,  N  the  total 
number  of  turns  in  the  secondary  coil,  A  the  area  of  the 
cross  section  of  the  primary,  and  S  the  current  through 
the  primary  in  electromagnetic  units.  Since  this  current 
is  measured  in  amperes,  it  is  necessary  in  practice  to 
call  S  the  intensity  of  the  primary  current  in  amperes 
and  divide  the  expression  by  lo  to  reduce  to  electro- 
magnetic  units.     The   formula   for   M'   then   becomes 

^-wnNAS  4  ^nNA  . 

Ihe  value is  constant  for  any  given 

TO  lO 

standard  coil,  and  once  determined  is  substituted  for 
M'  in  the  equation  MI  =  M'S. 

To  illustrate  the  process  of  determining  mutual  in- 
ductions by  this  method,  suppose  the  standard  coil  has 
the  following  dimensions : 

Number  of  turns  in  primary  per  centimeter. .  .  5.4 

Total  number  of  turns  in  secondary 1865 

Area  of  cross  section  of  primary 6  sq.  cm. 

The  value  of  is  75,870,  and  the  equation  for 

10 

mutual  induction  is  M  =  — ''— Now  suppose  that 


PRIMARY   AND   SECONDARY   COILS  41 

with  the  secondary  coil  at  12  cm.  from  the  zero  position 
the  breaking  of  a  primary  current  of  o.i  ampere  gives  a 
deflection  on  the  galvanometer  scale  of  5,  and  that  to 
secure  the  same  deflection  with  the  standard  coil  a  cur- 
rent of  6.8  amperes  must  be  broken  through  its  primary. 
Substituting  these  values  in  the  equation  we  obtain  for 
M  5,150,000.  By  repeating  this  procedure  the  values 
of  M  for  every  secondary  position  can  be  obtained. 

MI 

If  — —  is  a  true  expression  for  the  physiological  effect 

of  break  shocks,  evidently  with  L  constant  the  product 
MI  must  also  be  constant  so  long  as  it  represents  a  uni- 
form stimulus,  no  matter  how  the  value  of  M  may  be 
varied  by  shifting  the  secondary  coil.  Experiment  shows 
that  MI  does  remain  constant  for  a  constant  stimulus 
over  the  entire  field  of  the  inductorium,  except  that, 
when  an  iron  core  is  present,  it  varies  in  the  part  of  the 
field  directly  over  the  iron  core.  This  is  the  region  in 
which,  as  stated  in  a  former  paragraph,  the  value  of  L 
is  affected  by  the  presence  of  such  a  core.* 

If  a  constant  stimulus  gives  a  constant  value  of  MI, 
however  the  secondary  coil  may  be  shifted,  it  follows 
that  if  /  is  made  constant,  —  in  other  words,  if  a  fixed  cur- 
rent is  broken  through  the  primary  coil,  —  the  strengths 
of  stimulus  at  difTerent  secondary  positions  must  vary 

*  For  experimental  evidence,  see  Martin:  Amer.  Jour,  of  Physiol., 
190S,  xxii,  p.  124. 


42  INDUCTION  SHOCKS 

directly  as  the  values  of  M  for  those  positions.  By  de- 
termining these  values,  then,  we  provide  ourselves  with 
a  calibration  which  reveals  accurately  the  effect  on  stim- 
ulating strength  of  shifting  the  secondary  coil.  Such  a 
caUbration,  as  previously  stated,  is  a  necessary  basis  in 
any  scheme  for  the  quantitative  use  of  induction  shocks. 


CHAPTER  VI 

EFFECTS   PRODUCED   BY  AN  IRON  CORE  IN  THE 
PRIMARY   COIL 

Inasmuch  as  the  almost  universal  practice  in  physio- 
logical work  is  to  use  inductoria  with  iron  cores,  a  brief 
discussion  of  the  effects  of  such  cores  on  stimulation 
strengths  seems  desirable  at  this  point.  Thus  the 
method  becomes  at  once  applicable  to  inductoria  with 
iron  cores  as  well  as  to  those  not  provided  with  them. 

The  principal  effect  of  the  iron  core  is  that  which  has 
led  to  its  use,  namely  a  great  increase  in  the  number  of 
lines  of  force  surrounding  the  primary  coil,  with  a  cor- 
responding increase  in  the  intensity  of  the  stimuli  gen- 
erated. 

Another  effect  is  that  noted  in  a  previous  paragraph 
(p.  36),  of  altering  the  effectiveness  of  the  stimuH  gen- 
erated when  the  secondary  coil  is  directly  over  the  pri- 
mary, so  that  in  these  positions  MI  is  not  constant  for  a 
constant  stimulus.  The  method  of  correcting  the  caU- 
bration  for  this  effect  of  the  iron  core  is  given  in  Chap. 
VIII.  p.  58. 

The  iron  core  has  also  an  effect  upon  stimulation 
strength  due  to  its  magnetization  by  the  primary  current, 
an  effect  which  appears,  however,  only  when  primary 
currents  of  considerable  intensity  are  used.     Allowance 

43 


44  INDUCTION  SHOCKS 

for  this  effect  in  computing  the  values  of  MI  must 
be  made,  whenever  I  is  large,  by  introducing  a  correc- 
tion factor.  This  factor  can  be  obtained  without  diffi- 
culty by  the  use  of  the  balUstic  galvanometer,  since  the 
deflections  of  that  instrument  are  affected  by  core  mag- 
netization. Inspection  of  the  formula  MI  =  M'S  (p.  40) 
shows  that  so  long  as  M  and  M'  remain  constant,  /,  the 
current  through  the  primary  of  the  coil  under  examina- 
tion, must  vary  directly  as  S,  the  current  through  the 
primary  of  the  standard  coil.  This  relationship  is  found 
by  experiment  to  hold  in  ordinary  induction  coils  for 
values  of  /  up  to  o.i  ampere,  but  above  that  point  the 
value  of  5'  is  always  larger  than  the  equation  calls  for. 
In  other  words,  when  core  magnetization  is  present  the 
primary  current  produces  a  greater  deflection  than  it 
does  in  the  absence  of  this  effect.  The  variation  due  to 
the  magnetization  of  the  core  is  not  very  difficult  to 
correct,  because,  as  repeated  experiment  has  shown,  the 
ratio  between  the  actual  values  of  I  and  those  computed 
from  the  values  of  S  depend  upon  an  easily  determined 
factor  which  is  constant  for  any  given  iron  core. 

To  determine  this  factor  some  position  of  the  second- 
ary coil  must  be  selected  at  which  primary  currents  up 
to  I  ampere  give  galvanometer  deflections  not  greater 
than  the  entire  scale.  With  the  secondary  in  this  posi- 
tion primary  currents  of  increasing  intensity,  beginning 
at  about  o.oi  ampere,  are  broken,  and  the  deflections 


EFFECTS  OF  IRON  CORE  IN  THE  PRIMARY  COIL  45 


produced  by  each  carefully  noted.  Then  with  the  stand- 
ard inductorium  the  values  of  5  giving  these  same  de- 
flections are  determined.  Although  at  first  the  ratio 
of  5  to  /  remains  constant,  as  the  values  of  /  begin  to 
exceed  o.i  ampere  the  ratio  steadily  increases.  It  is 
evident,  therefore,  that  large  currents  are  producing 
relatively  greater  deflections  than  small  ones.  By  mul- 
tiplying the  different  values  of  5  by  the  ratio  of  5  to  /, 
which  was  constant,  we  obtain  a  series  of  computed  values 
of  /  representing  the  currents  which  would  be  required 
to  produce  the  observed  galvanometer  deflections  if  no 
iron  core  were  present.  These  are,  of  course,  the  values 
of  /  which  are  to  be  employed  in  computing  the  strengths 

of  stimuli  according  to  the  expression  —j-  - 

Table  I,  column  3,  gives  the  values  of  /  computed 
from  a  series  of  observed  values  of  /  and  5  in  actual 

experiments. 

TABLE   I 


Value  of  /  ob- 
served in  am- 
peres. 

Value  of  S  ob- 
served. 

Value  of  /  com- 
puted in  am- 
peres. 

Ratio  computed 
value  of  /  to  its 
observed  value. 

Decimal  part 

of  ratio  divided 

by  observed 

value  of  /. 

O.OI 

0.005 

O.OI 

1 .0 

0.05 

0.025 

0.05 

I  .0 

O.IO 

0.05 

0. 10 

1 .0 

0.20 

0.1044 

0.2088 

1.044 

22 

0.30 

0.1507 

0.3194 

1.065 

217 

0.40 

0 . 2  1 80 

0.4360 

1.090 

225 

0.50 

0.2782 

0.5564 

1. 113 

226 

0.60 

0.3306 

0.6702 

I.  132 

22 

46  INDUCTION  SHOCKS 

To  derive  the  equation  for  obtaining  I  computed  when 
/  observed  is  known  we  determine  in  a  series  of  experi- 
ments the  ratios  of  /  computed  to  /  observed  (see  column 
4  of  the  table).  If  now  the  decimal  part  of  each  ratio  is 
divided  by  its  corresponding  value  of  /  observed,  a  con- 
stant is  obtained  which  represents  the  number  by  which 
/  observed  must  be  multiplied  to  obtain  this  decimal  part 
of  the  ratio.  This  constant  is  shown  in  column  5. 
After  the  constant  is  found  it  is  used  for  computing  / 
according  to  the  formula  /^  =  /o  X  (i  -}-  Kh).  In  this 
formula  /c  is  the  computed  value  of  I,  h  is  its  observed 
value,  and  K  is  the  constant,  —  in  the  case  cited  in  the 
table  equaling  .22. 

The  method  of  correcting  for  the  magnetization  of 
the  iron  core  is  given  in  detail  since,  in  spite  of  the  abun- 
dant theoretical  justification  for  the  omission  of  the 
iron  core,  especially  where  quantitative  estimations  are 
sought,  for  the  practical  purposes  of  the  physiologist 
the  inductorium  as  commonly  used,  with  the  iron  core 
present,  is  usually  to  be  preferred.  The  intensity  of 
stimulus,  other  factors  being  equal,  is  at  least  five  times 
greater  with  the  iron  core  than  without  it  in  inductoria 
of  the  usual  type.  This  increased  efficiency  makes  it 
possible  to  obtain  with  primary  currents  of  moderate 
intensity  as  strong  stimuli  as  the  physiologist  ordinarily 
requires.  The  use  of  moderate  primary  currents  is  of 
great  importance  in  quantitative  estimations  of  indue- 


EFFECTS  OF   IRON   CORE   IN  TPIE   PRIMARY    COIL     47 

tion  shocks,  since  thereby  is  avoided  that  heavy  sparking 
at  the  contacts  which  always  accompanies  the  break  of 
a  current  of  high  intensity,  and  which  affects  the 
intensity  of  the  stimulus  in  a  manner  that  cannot  be 
foretold. 

When  the  secondary  coil  of  an  inductorium  is  moved 
from  the  zero  position  until  nearly  clear  of  the  primary 
coil,  it  enters  a  "critical  region"  where  small  changes  in 
position  are  accompanied  by  great  changes  in  the  in- 
tensity of  the  stimuli  given  by  the  instrument.  The 
impression  seems  to  prevail  among  physiologists  that 
inductoria  having  iron  cores  show  so  much  greater  vari- 
ations of  intensity  in  this  "critical  region"  than  do  those 
without  iron  cores  as  to  make  the  omission  of  the  iron 
core  a  distinct  advantage  in  many  experiments.  As  a 
matter  of  fact,  however,  Kronecker  inductoria,  such  as 
are  used  in  most  physiological  laboratories,  show  for 
given  changes  in  secondary  position  in  the  "critical 
region"  greater  variations  in  stimulation  intensity  with 
cores  removed  than  with  cores  present.  This  is  appar- 
ent when  the  Kronecker  graduations  of  such  coils  are 
compared  with  the  calibrations  made  for  them  by  the 
method  of  the  present  work  (see  p.  55).  In  the  prep- 
aration of  the  Kronecker  graduations  the  iron  cores 
were  withdrawn  from  the  instruments.  For  the  cali- 
brations made  in  connection  with  this  work  the  iron 
cores  were  in  place. 


48 


INDUCTION  SHOCKS 


TABLE  II 

Effect  of  the  Iron  Core  on  the  Rate  of  Change  of  Stimulation 
Intensity  in  the  "  Critical  Region  "  of  the  Inductorium 


Position  of  sec- 

Iron core  absent. 

Iron  core  present. 

ondary  in  cen- 
timeters. 

Kronecker 
graduation. 

Percentage  de- 
crease per  centi- 
meter. 

Author's  cali- 
bration. 

Percentage  de- 
crease per  centi- 
meter. 

8 
9 

lO 

II 

12 

13 
14 
15 
i6 

17 
i8 

19 

6190 
5150 
4150 
3250 
2375 
1570 
1000 
625 

435 
310 
230 
178 

17 
19 
21 
27 

33 
36 
37 
30 
28 

25 

22 

0 
4 
7 
0 

9 
3 
5 
4 
7 
7 
7 

6240 

5340 

4500 

3600 

2640 

1920 

1270 

860 

600 

455 

350 

280 

14.4 

15-7 

20 

26.7 

27-3 

33-8 

32.1 

30-3 
24.2 
23.1 
20.0 

Table  II  gives  a  comparison  of  the  calibrations  in  the 
"critical  region"  of  one  inductorium  made  without  and 
with  the  iron  core.  The  primary  coil  of  this  instrument 
was  14  cm.  long.  The  table  shows  clearly  that  the  rate 
of  decrease  of  stimulation  intensity  from  point  to  point 
is  greater  when  the  iron  core  is  absent  than  when  it 
is  present.  Table  III  is  the  record  of  experimental 
verification  of  the  same  fact.  Stimulation  intensities 
were  compared  in  these  experiments  according  to  the 
V.  Fleischl  method  (p.  56),  namely  by  comparing  the 
primary  currents  required  to  produce  stimuli  of  equal 
value  with   the   secondary  coil   at  different  positions. 


EFFECTS  OF  IRON  CORE  IN  THE  PRIMARY   COIL     49 

According  to  this  method  increases  in  the  primary  current 
represent  corresponding  decreases  in  the  stimulating 
efficiency  of  the  inductorium. 


TABLE   III 

Experimental  Proof  that  Stimulation  Intensity  shows  Greater 
Variation  in  the  "  Critical  Region  "  when  the  Iron  Core  is 
Absent  than  when  it  is  Present.     Break  Shocks 


Position  of 
secondary 
in  centi- 
meters. 

Iron  core  absent. 

Iron  core  present. 

Date  of  experiment. 

Primary 
current, 
amperes. 

Per- 
centage 
increase 
in  cur- 
rent. 

Primary 
current, 
amperes. 

Per- 
centage 
increase 
in  cur- 
rent. 

Dec.  21,  1906 

Dec.  24,  1906 

Apr.  15,1907 

8.0 
12.0 
16.0 

8.0 
12.0 
16.0 

8.2 

11.28 

12.45 

14.0 

16.2 

0.0195 

0.0505 

0.260 

0.00576 

0.01523 

0.091 

0.017 

0.035 

0.0535 

0.  107 

0.2485 

159 
415 

164 
432 

107 

50 

100 

132 

0.001S7 

0 . 00463 

0.022 

0 . 0008 

0.00107 

0. 00934 

0.0036 

0.0063 

0.0092 

0.016 

0.034 

148 
375 

146 
374 

75 

46 

74 

112 

CHAPTER  VII 

COMPARISON   OF  ONE  COIL  WITH   ANOTHER  — THE 
VALUE  OF  L 

We  have  seen  (p.  41)  that  in  any  given  inductorium, 
after  allowing  for  certain  exceptions  due  to  the  iron  core, 
if  one  is  present,  the  strengths  of  stimuli  produced  by  a 
given  primary  current  with  the  secondary  coil  at  various 
positions  are  directly  proportional  to  the  mutual  induc- 
tions for  those  positions.  When,  however,  the  attempt 
is  made  to  compare  the  stimuli  generated  by  one  in- 
ductorium with  those  produced  by  another,  it  is  at 
once  apparent  that  the  relation  between  stimulating 
value  and  mutual  induction  holds  only  for  stimuli  pro- 
duced by  the  same  instrument.  This,  indeed,  was  rec- 
ognized by  Helmholtz,  who  pointed  out  the  necessity  of 
including  in  the  expression  for  stimulating  value  the 
factor  L,  whereby  to  take  account  of  the  influence  of 
inductorium  construction.  This  factor,  according  to 
Helmholtz,  is  dependent  on  the  inductance  of  the  sec- 
ondary coil,  and  is  to  be  derived,  therefore,  from  the 
expression  for  inductance.     The  common  formula  for 

the  mductance  of  a  coil  is  L  =  — - — '  in  which  L  is  the 

t 

50 


COMPARISON   OF   ONE   COIL   WITH   ANOTHER         51 

inductance  of  the  coil,  A  its  mean  cross  section,  W  the 
number  of  turns  of  wire  composing  it,  and  /  its 
length. 

When,  in  the  course  of  developing  this  method  of 
measuring  stimuli,  the  attempt  was  made  to  apply  the 

MI 
above  expression  for  L  in  the  formula     - '  the  curious  ob- 
servation resulted  that  it  applied  perfectly  with  some 
inductoria  and  not  with  others.     That  is  to  say,  when 
equal  stimuli  were  generated  by  means  of  different  in- 

,  MI 
ductoria,  equal  values  of  — -  were  given  by  some,  but 

not  by  all,  of  the  instruments  compared.  Upon  analyz- 
ing the  reason  for  the  difference  the  following  fact  came 

out  clearly;  equal  values  of  y-  were  given  by  those  in- 

ductoria  whose  secondary  coils  had  the  same  niimher  oj 
turns  oj  wire  per  centimeter  oj  lengthy  regardless  oj  the  total 
number  oj  turns  oj  wire;  unequal  values  were  given  by 
those  inductoria  whose  secondaries  had  different  nutnbers 
oj  turns  per  centimeter  oj  length.     If  we  look  now  at  the 

expression  for  L  given  above,  i.e.,  L  —  — - — '  and  sepa- 
rate within  it  the  factor  of  turns  per  unit  of  length,  the 

W 
expression  reads  L  =  AW  X  —■      The  experimental  re- 

t 

suits  showed  as  stated  above  that  in  all  the  inductoria 


52  INDUCTION  SHOCKS 

W 
having  the  same  value  of  — '  namely  the  same  number 

L 
of  turns  per  centimeter,  the  expression  L  =  AW  might 

be  substituted  for  the  expression  L  =  — —  and  equal 

MI 

values  of for  equal  stimuli  would  be  given.     The 

next  step  was  to  see  whether  those  inductoria  which  for- 
merly gave  non-concordant  results  would  give  concordant 
ones  if  for  the  value  of  L  the  expression  AW,  namely  the 
product  of  the  cross  section  of  the  secondary  by  the  num- 
ber of  turns  in  it,  were  used.  It  was  found  that  when  this 
was  done  all  the  inductoria  examined  gave  for  equal  stim- 

MI 

uli  corresponding  values  of  ■— -'  regardless  of  the  dimen- 

sions  of  the  coils,  but  subject  to  a  certain  restriction  as 
to  secondary  resistance  to  be  discussed  later  (p.  78). 
In  order  to  bring  this  point  out  clearly  some  of  the  ex- 
periments upon  which  it  is  based  are  cited  below  (Table 
V).  The  inductoria  used  are  described  in  Table  IV. 
In  this  table  only  those  inductoria  are  considered  whose 
secondaries  have  different  numbers  of  turns  per  centi- 
meter, since  only  by  them  can  be  determined  which  of 
the  two  expressions  for  L  is  correct.  In  all  the  experi- 
ments, comparisons  were  made  between  the  various  in- 
ductoria and  a  single  one  known  as  coil  B.  This  is  a 
large  inductorium  with  a  Kronecker  calibration  whose 


COMPARISON   OF   ONE  COIL   WITH   ANOTHER         53 

secondary  has  800  turns  per  centimeter;  it  was  selected 
as  a  basis  of  comparison  merely  for  convenience. 

In  Table  IV,  columns  5  and  6,  are  given,  for  the  differ- 
ent inductoria  examined,  the  values  of  L  =  AW  and 

A]r- 

L  =  — - —     To  simplify  the  comparisons  between  the 

various  coils  the  values  of  — - —  as  given  in  Table  IV 

were  all  divided  by  800,  the  number  of  turns  per  centi- 
meter in  the  secondary  of  coil  B,  thus  making  the  value  of 
L  for  coil  B  the  same  by  either  formula.  These  values 
are  set  down  in  column  7  of  the  table.  To  bring  the 
final  results  into  convenient  denominations  these  figures 
and  also  those  in  column  5  were  divided  by  100.  It  is 
understood,  of  course,  that  these  divisions,  made  purely 
for  convenience,  in  no  wise  modify  the  relations  between 
the  coils. 

In  Table  V  are  set  down  the  experimental  results  of 
the  comparisons  between  the  various  inductoria.  Since 
details  would  only  confuse,  they  are  omitted.  The  fig- 
ures presented  in  the  table  show  clearly  that  the  proper 

AW- 
expression  for  Lis  AW  rather  than — r— • 

If 


54 


INDUCTION  SHOCKS 


TABLE   IV 
Description  of  inductoria  used  in  establishing  expression  for  L 


Coil. 

Length 
of  sec- 
ondary 
coil. 

Turns  in 

secondary 

coil. 

Cross  sec- 
tion of  sec- 
ondary coil. 

Cross  sec- 
tion X  turns 
in  secon- 
dary coil. 

Cross  section  X 

turns  in  sec.^ 

length 

Column  6 

divided  by 

800. 

B 
C 
F 
H 

N 

cm. 

13 
7-4 

13-5 
9-3 
9-3 

10,350 
4.830 
3,000 
6,000 
8,000 

sq.  cm. 
17.6 

22 

iS-4 
16.6 
17.8 

182,000 
105,000 
46,000 
100,000 
142,000 

145,000,000 
69,500,000 
10,250,000 
64,300,000 

122,500,000 

182,000 
87,000 
12,800 
80,000 

153,000 

TABLE  V 
Demonstrating  that  the  expression  for  L  should  he.  AW  rather 

AW 
I 


than 


MI      .,  „ 
-J-  coil  B. 

Coil. 

MI 
AW 

MI 

AW^ 

1X800 

MI 
L 

coilB. 

Coil. 

MI 
AW' 

MI 

AW 

1X800 

8 
12.6 
II. 4 
28.2 

17 
2.6 

30.5 
64 

C 

F 
H 

1-1 
13 

II. 7 
28 
16.4 

2.8 

30.9 
61. 1 

4-5 

7.6 

6.9 

100 

57 

3-5 

38.6 

76.4 

7-5 

7 

5-3 

2-57 
30.5 
64 
10.  2 

7-5 

H 

N 

7-5 
7.2 

5-3 
2.43 

28.6 

60 

10.4 
7 

9-4 

9 

6.6 

2.25 
26.5 
S6 
9-7 
6.5 

CHAPTER  VIII 

THE   PREPARATION    OF   A    CALIBRATION    SCALE   FOR 
BREAK   SHOCKS 

In  previous  chapters  the  methods  of  obtaining  the 
individual  factors  making  up  the  expression  for  break 
stimukition  strength  have  been  discussed  in  detail  To 
show  how  these  methods  are  put  into  practice  in  pre- 
paring an  inductorium  for  quantitative  use  is  next  in 
order.  The  first  step  is  the  determination  of  the  mutual 
inductions  by  the  method  hitherto  described,  for  a 
series  of  positions,  preferably  not  more  than  2  cm. 
apart,  along  the  scale.  If  the  instrument  to  be  cali- 
brated is  without  the  iron  core  these  measurements 
should  be  taken  from  the  zero  position  outward;  if  an 
iron  core  is  present  there  is  no  advantage  gained  by 
determinations  of  mutual  induction  for  secondary  posi- 
tions in  the  region  where  the  secondary  coil  overlaps 
the  primary.  Having  determined  these  values,  each  is 
divided  by  L,  the  product  of  the  cross  section  by  the 
number  of  turns  of  the  secondary  coil.  The  mean 
cross  section  must  be  determined  with  great  care,  a 
rather  difficult  procedure  in  completed  inductoria,  and 
one  which  ought  to  be  carried  out  in  connection  with 
their  manufacture. 

5S 


$6  INDUCTION  SHOCKS 

In  order  that  the  final  stimulation  units  may  be  of 
convenient  size  the  value  of  L  which  has  been  adopted 
in  this  scheme  is  not  the  direct  product  of  the  cross 
section  by  the  number  of  turns  of  the  secondary,  but  is 
that  product  divided  by  loo.  Having  determined  this 
value,  the  mutual  inductions  previously  estabHshed  are 
divided  by  it.  The  resulting  figures  are  the  "calibra- 
tion numbers"  for  the  particular  secondary  positions  to 
which  they  apply.  To  determine  the  numbers  for  in- 
termediate positions  those  determined  as  above  are  plot- 
ted on  a  rather  large  scale  on  coordinate  paper  and  a 
smooth  curve  is  drawn  connecting  them.  Since  the 
mutual  induction  necessarily  diminishes,  not  by  fits  and 
starts,  but  smoothly,  as  the  secondary  is  moved  out- 
ward, such  a  curve,  if  carefully  made,  will  indicate  the 
calibration  numbers  for  intermediate  positions  with  a 
high  degree  of  accuracy. 

To  prove  the  accuracy  of  the  caHbration  the  method 
of  V.  Fleischl  is  employed  (p.  i8)  in  which  the  minimal 
contraction  of  a  frog's  gastrocnemius  is  used  as  the  index 
of  a  constant  stimulus.  In  detail  this  procedure  as  carried 
out  by  myself  was  as  follows :  The  freshly  isolated  gas- 
trocnemius was  suspended  by  its  attached  femur  in  a 
moist  chamber,  and  its  lower  end  connected  by  a  small 
copper  wire  to  a  muscle  lever  whose  effective  weight  was 
about  lo  gm. ;  the  muscle  was  not  af  terloaded.  The  lever 
had  a  magnification  of  about  ten,  and  its  point  pressed 


CALIBRATION  SCALE  FOR  BREAK  SHOCKS  57 

lightly  upon  a  smoked  drum.  The  minimal  contraction 
could  be  detected  without  diiliculty,  since  the  whole  appa- 
ratus was  made  rigid  enough  for  the  shghtest  movement 
of  the  muscle  to  show  itself  at  the  end  of  the  lever. 
Connection  between  the  muscle  and  the  terminals  of  the 
secondary  coil  was  by  means  of  two  platinum  needles 
soldered  to  tine  copper  wires  leading  from  the  secondary 
terminals.  These  needles  were  thrust  directly  through 
the  muscle  tissue,  —  one  about  5  mm.  below  its  origin, 
the  other  the  same  distance  above  the  distal  tendon, 
both  in  the  same  vertical  plane.  By  this  method  of 
connecting  the  muscle,  variations  in  the  secondary  re- 
sistance aside  from  those  in  the  tissue  itself  were  avoided. 
At  least  half  an  hour  was  allowed  to  elapse  after  the 
muscle  was  hung  in  position  before  stimulation  was 
begun;  in  order  that  summation  might  not  enter,  the 
shortest  interval  allowed  between  successive  stimuli  was 
ten  seconds;  to  avoid  fatigue  the  strength  of  stimulus 
used  was  always  kept  as  near  minimal  as  possible.  The 
results  of  repeated  experiments  show  that  under  these 
conditions  a  high  degree  of  constancy  is  usually  main- 
tained during  the  interval,  about  three  hours,  required 
for  a  single  experiment.  That  each  experiment  be  com- 
plete in  itself  is,  of  course,  necessary,  since  no  means  has 
suggested  itself  for  obtaining  a  response  which  shall 
remain  constant  through  a  period  of  successive  days. 
To  have  conditions  uniform  the  electrode  nearer  to  the 


58  INDUCTION  SHOCKS 

origin  of  the  muscle  was  in  most  cases  made  the  cathode. 
With  the  minimal  contraction  of  the  muscle  as  the  index, 
the  primary  current  necessary  to  arouse  it,  measured  in 
amperes,  is  determined  with  the  secondary  coil  in  various 
positions.  To  allow  for  variations  in  irritabiHty  of  the 
tissue  the  experiment  should  be  repeated  a  number  of 
times.  If  the  caHbration  is  carefully  made  in  the  be- 
ginning it  will  be  found  that  in  each  individual  experi- 

M  ^  .  .  T 

ment  the  product  —  X  /,  —  primary  current  times  cah- 

bration  number,  —  is  virtually  constant,  showing  that 
the  calibration  is  correct. 

Should  the  inductorium  being  calibrated  have  an  iron 
core,  there  still  remains  the  estabhshment  of  calibra- 
tion numbers  for  the  region  where  the  secondary  coil 
overlaps  the  primary.  These,  however,  can  easily  be 
determined  by  extending  the  experiments,  just  de- 
scribed for  proving  the  caUbration,  to  cover  this  part  of 

M  .  .  . 

the  field.     The  value  of  —  X  /  is  established  m  any 

M  . 
given  experiment  from  the  part  of  the  field  where  —  is 

known,  that  is,  where  the  calibration  has  already  been 
worked  out.  Since  this  is  constant  so  long  as  the  stim- 
ulus is  unchanged  a  determination  of  the  primary  current, 

M 
I,  for  this  stimulus,  in  the  region  where  —  is  unknown, 


CALIBRATION  SCALE   FOR  BREAK   SHOCKS  59 

yields  at  once  data  for  computing  —  •      By  averaging 

several  experiments  this  part  of  the  field  can  be  cali- 
brated with  sufficient  accuracy. 

It  must  be  stated,  however,  that  in  the  innermost 
part  of  the  field,  including  about  half  of  the  length  of 
the  primary  coil  from  zero  outward,  the  calibration  num- 
bers determined  by  the  v,  Fleischl  method  will  be  found 
to  dififer  somewhat  according  as  the  tissue  used  as  an 
indicator  has  high  or  low  resistance,  high  resistances 
showing  larger  calibration  numbers  than  low  ones.  For 
this  reason  it  is  desirable  to  avoid  using  this  region  in 
work  which  requires  a  high  degree  of  accuracy,  unless 
a  calibration  has  been  previously  worked  out  for  the 
resistance  actually  to  be  employed.  Experience  shows 
that  occasions  when  it  is  necessary  to  use  the  first  5  or 
6  centimeters  of  the  scale  are  of  rare  occurrence  in  most 
kinds  of  experimental  work. 


CHAPTER  IX 

THE  MAKE  AND  BREAK  OF  THE  PRIMARY  CIRCUIT 

From  the  beginning  of  the  use  of  induction  shocks  for 
stimulating  Hving  tissues  investigators  have  recognized 
that  the  physiological  intensities  of  these  shocks  are 
markedly  affected  by  the  manner  of  making  or  breaking 
the  primary  circuit.  Helmholtz  *  called  attention  to 
this  fact  in  his  study  of  induced  currents,  and  in  the  dis- 
cussion of  the  variable  factors  to  be  considered  in  the 
attempt  to  measure  induction  shocks  (p.  14),  I  pointed 
out  that  the  manipulation  of  the  primary  key  is  a  vari- 
able whose  influence  cannot  be  mathematically  deter- 
mined, and  which,  therefore,  must  be  made  as  uniform 
as  possible. 

Before  entering  upon  a  discussion  of  means  whereby 
the  manipulation  of  the  primary  make  and  break  key 
can  be  made  uniform,  it  is  desirable  to  point  out  briefly 
the  manner  in  which  variations  in  the  break  and  make 
of  the  primary  circuit  modify  stimulating  intensities. 

In  the  account  of  the  theoretical  basis  for  the  break 

M 
shock  formula,  Z  =  -y  I   (p.  34),  the  statement  was 

*  Helmholtz:  Poggendorf's  Annalen  der  Physik  und  Chemie,  185 1, 
Ixxxiii,  p.  538. 

60 


THE  MAKE  AND  BREAK  OF  THE  PRIMARY  CIRCUIT   6 1 

made  that  this  expression  applies  exactly  only  when  the 
break  is  instantaneous,  although  it  holds  relatively  so 
long  as  the  time  occupied  by  the  break  docs  not  vary. 
Since  this  in  turn  depends  on  the  duration  of  the  spark, 
our  present  inquiry  resolves  itself,  so  far  as  break  shocks 
are  concerned,  into  a  study  of  the  conditions  governing 
contact  sparking. 

The  duration  of  the  spark  at  a  broken  primary  con- 
tact depends  in  part  upon  the  intensity  of  the  primary 
current,  in  part  upon  the  amount  of  volatilization  occur- 
ring at  the  contact,  and  in  part  upon  the  speed  with 
which  the  points  are  separated.  This  last  factor  ex- 
plains why  keys  operated  by  hand  cannot  be  depended 
upon  to  give  uniform  results,  and  why  some  form  of 
automatic  key  is  required,  since  only  thus  can  a  uniform 
speed  of  separation  be  secured.  Moreover,  ordinary 
mercury  keys  cannot  be  depended  on  even  when  oper- 
ated automatically,  because  of  the  tendency  of  mercury 
when  not  absolutely  clean  to  chng  in  drops  and  thus 
vary  the  speed  with  which  the  contact  points  actually 
separate.  In  practically  all  keys  there  is  some  volatil- 
ization; platinum  contacts  giving  the  least,  ordinary 
mercury  contacts  the  most.  It  is  impracticable  to  use 
always  primary  currents  of  a  single  intensity;  but,  in 
primary  currents  not  exceeding  i  ampere,  the  variation 
is  too  slight  to  be  of  practical  importance. 

The  making  of  a  primary  circuit  is  not  attended  with 


62  INDUCTION  SHOCKS 

sparking,  so  that  the  sources  of  error  for  makes  are  not 
the  same  as  for  breaks.  As  a  circuit  is  made  the  re- 
sistance falls  from  infinity  to  the  resistance  of  the  closed 
circuit  itself.  It  is  during  the  change  from  the  first  of 
these  resistances  to  the  second  that  the  secondary  cur- 
rent is  induced.  The  more  nearly  instantaneous  the 
change,  the  greater  is  the  physiological  intensity  of  the 
induced  current.  In  hand-operated  metal-contact  keys 
there  can  be  no  assurance  that  the  contact  points  will  be 
pressed  together  with  the  same  firmness  twice  in  succes- 
sion, so  that  to  secure  uniformity  of  contact  automatic 
keys  are  required  for  make  shocks  as  well  as  for  breaks. 
A  further  and  more  serious  defect  in  metal-contact  keys 
for  make  shocks  is  their  liability  to  rebound  slightly,  or 
to  slip  sidewise,"thus  giving  not  a  single  clean-cut  make, 
but  a  succession  of  make,  break,  and  make.  So  con- 
stantly has  this  defect  shown  itself  in  my  experiments, 
even  with  carefully  constructed  automatic  metal-contact 
keys,  that  I  have  found  it  necessary  to  use  mercury  con- 
tacts altogether  in  studying  make  shocks. 

The  considerations  stated  above  lead  to  the  following 
conclusions:  That  hand-operated  keys  are  not  to  be  de- 
pended on  for  uniform  makes  and  breaks ;  that  for  break 
shocks  platinum  contacts  are  to  be  preferred  to  mercury 
because  of  their  less  volatilization,  while  for  make 
shocks,  on  account  of  the  rebound  or  side-slip  of  metal 
contacts,  mercury  affords  the  only  trustworthy  contact. 


THE  MAKE  AND  BREAK  OV  THE  PRIMARY  CIRCUIT   63 


It  is,  of  course,  wholly  undesirable  to  ecjuip  the  pri- 
mary circuit  with  two  keys,  —  one  of  mercury  to  be 
used  for  making  the  circuit,  and  another  of  platinum  for 
breaking  it.  I  shall  describe,  therefore,  an  automatic 
make  and  break  key  with 
mercury  contacts  which  has 
been  proved  by  several  years' 
experience  to  give  uniform 
breaks  and  makes.* 

The  key  consists  of  a  block 
of  vulcanite  30  mm.  long, 
20  mm.  wide,  and  25  mm. 
deep,  having  cut  in  it  two 
vertical  chambers  (see  Fig. 
11),  one  (a)  rectangular,  20 
mm.  long,  8  mm.  wide,  and 
20  mm.  deep;  the  other  (b) 
cylindrical,  6  mm.  in  diameter 
and  20  mm.  deep.  A  hole,  c 
(Fig.  11),  3  mm.  in  diameter, 
is  bored  through  from  one  of 


Fig.  II.  Diagram  illustrating 
the  principle  of  the  vulcanite 
knife-blade  key.  The  front  of 
the  block  is  broken  away  to 
show  the  relations  of  the  parts 
within  the  chamber,  a.  a  and 
b,  mercur}'  chambers;  c,  open- 
ing between  a  and  b;  d,  vul- 
canite knife  blade  supported 
upon  axis,  0,  which  rotates 
within  collar,  e. 


these  cavities  to  the  other  at 
a  depth  of  about  16  mm.      Each  of  the  chambers  is  in 
electrical  communication  with  a  l)inilinL:;  post,  and  when 
filled  with  mercury  they  arc  in  electrical  communication 
with  each  other  through  the  connecting  hole,  c. 
*  Martin:   .\m.  Jour,  of  Physiol.,  1910,  xxvi,  p.  i8i. 


64  INDUCTION  SHOCKS 

A  strip  of  vulcanite,  d  (Fig.  ii),  i8  mm.  long,  8  mm. 
wide,  and  i  mm.  thick,  flat  on  one  side  and  on  the 
other  tapered  toward  the  edges,  is  supported  at  the  top  of 
the  block  by  a  horizontal  rod  working  freely  in  a  collar, 
e  (Fig.  ii),  in  such  fashion  as  to  press  closely  against 
the  inner  surface  of  the  cavity,  a,  and  when  rotated 
about  its  axis  of  support  to  cover  or  uncover  the  open- 
ing, c.  When  the  vulcanite  strip  is  brought  over  the 
opening,  it  cuts  the  mercury  connection  between  cavi- 
ties a  and  h,  and  therefore  breaks  any  electric  circuit 
which  may  include  them.  This  method  of  breaking  a 
circuit  has  many  points  in  its  favor.  The  break  cannot 
be  delayed  through  the  tendency  of  mercury  drops  to 
cling  together,  for  the  severance  of  the  mercury  column  is 
not  the  withdrawal  of  one  mass  of  mercury  from  another, 
but  is  the  forcible  interposition  of  a  nonconductor  in  the 
path.*  Moreover,  the  vulcanite  strip  cuts  off  not  only 
the  liquid  mercury,  but  if  it  fits  tightly,  as  it  should,  cuts 
off  as  well  any  mercury  vapor  that  may  be  formed. 
Thus  the  effect  of  volatihzation  of  mercury  is  minimized. 
Since  the  point  where  the  break  occurs  is  beneath  a  con- 
siderable depth  of  mercury,  air  does  not  have  access  to  it, 
and  oxidation  does  not  occur.  I  have  found,  as  a  matter 
of  fact,  that  the  same  mercury  may  be  used  in  one  of 
these  keys  for  months  without  any  appreciable  varia- 
tion in  the  effectiveness  of  the  break. 

*  A  device  employing  the  same  principle  was  described  by  Lombard 
in  1902:  Am.  Jour,  of  Physiol.,  1902,  viii,  p.  xx. 


THE  MAKE  AND  BREAK  OF  THE  PRIMARY  CIRCUIT  65 

When  the  vulcanite  strip  is  so  rotated  as  to  uncover  the 
hole,  c,  the  mercury  in  the  two  cavities  reunites  and  thus 
makes  the  circuit.  The  reunion  of  the  separated  mer- 
cury masses  should  take  place  as  smoothly  as  possible. 
To  bring  this  about,  the  vulcanite  knife  blade  is  tapered 
at  the  edges  so  that  it  may  plough  through  the  mercury 
with  as  little  disturbance  as  possible. 


Fig.  12.  Diagram  of  the  operating  device  for  the  knife-blade  key; 
vertical  view.  /,  triangle  of  brass  bearing  slits,  g,  g',  and  wings,  w,  w', 
rotating  about  axis,  0;  /,  /',  actuating  springs;  k,  k',  levers  for  bringing 
tension  upon  springs,  and  at  the  same  time  operating  release,  1;  m,  m', 
stops  for  limiting  motion  of  knife  blade. 


The  Operating  Device.  To  secure  uniformity  of  ac- 
tion the  vulcanite  blade  must  be  operated  automati- 
cally, hand  operation  being  liable  to  wide  variations  in 
the  speed  with  which  the  contact  is  made  or  broken. 
The  method  adopted  in  this  instrument  is  illustrated  by 
the  diagrams  (Figs.  12  and  13).  The  axis  of  rotation  of 
the  blade,  0  (Figs.  11  and  12),  after  passing  through  the 


66 


INDUCTION  SHOCKS 


supporting  collar,  e  (Fig.  ii),  is  fastened  into  a  trian- 
gular sheet  of  brass,  /  (Fig.  12),  from  whose  apex  pro- 
ject horizontally  two  brass  arms,  w  and  w'\  these  are 

bent  at  right  angles  at 
their  outer  ends,  as  shown 
in  Fig.  13.  From  the  tip 
of  each  of  these  arms  a 
coiled  spring,  /  and  I'  (Fig. 
12),  extends  down  to  the 
end  of  a  lever,  k  and  k' . 
Each  spring  consists  of 
twenty-seven  turns  of 
spring  brass  wire,  0.6  mm. 
in  diameter.  The  length 
of  the  spring  is  about  16 
mm.,  and  the  outside  di- 
ameter of  the  coil  5  to  6 
Fig.  13.  Diagram  of  the  operating  ^^  r^^^  depression  of 
device   for    the    knife-blade    key; 

horizontal  view.    Significance  of  either  lever  puts  the  spring 

letters  the  same  as  in  Figs.  11  and    connecting    with    it    under 
12.     s,  cavity  in  base  for  holding  .  ^  ^  ^ 

short-circuiting  device.  tension  and  tends  to  draw 

downward  the  correspond- 
ing arm,  rotating  the  vulcanite  blade  with  it.  To  pre- 
vent movement  of  the  blade  until  the  spring  has  been 
put  under  a  certain  degree  of  tension,  two  sHts,  g  and  g' , 
are  cut  into  the  lower  edge  of  the  triangle,  /.  A  re- 
leasing device,  i,  is  pressed  upward  against  the  lower 


THE  MAKE  AND  BREAK  OF  THE  PRIMARY  CIRCUIT    67 

edge  of  /  by  a  stout  spring,  in  such  fashion  that  when 
either  slit  is  engaged/  is  prevented  from  moving.  Each 
of  the  levers,  k  and  k,'  bears  at  its  tip  an  arm,  r,  r'  (Fig. 
13),  which  presses  upon  the  releasing  device,  and  when 
the  lever  is  depressed  to  a  certain  point  disengages  it, 
allowing  the  blade  to  rotate.  The  amount  of  motion 
of  the  blade  is  limited  by  setting  two  posts,  m  and  ;;/', 
at  such  positions  that  the  lower  apices  of  /  strike  them 
when  sufficient  movement  has  occurred. 

After  experimenting  with  various  operating  devices  the 
one  described  above  has  been  adopted  as  combining  the 
greatest  number  of  desirable  features  with  the  fewest 
defects.  The  two  levers,  k  and  k' ,  which  are  depressed 
alternately  for  making  and  breaking  the  circuit,  are  so 
placed  as  to  lie  naturally  under  the  first  and  second 
fingers  of  either  the  right  or  the  left  hand.  The  springs, 
/  and  /',  need  not  be  stiff,  hence  little  pressure  need  be 
exerted  upon  the  levers,  and  there  is  correspondingly 
little  fatigue  from  continuous  operation  of  the  key. 
The  springs  are  brought  under  tension  only  during  the 
use  of  the  instrument;  when  it  is  not  in  use,  they  hang 
free.  Thus  their  stiffness  does  not  vary  with  the  lapse 
of  time,  as  would  be  the  case  were  one  or  the  other  under 
constant  tension. 

The  Short-circuiting  Device.  A  desideratum  in  any 
key  which  is  to  be  used  for  stimulating  tissues  with  single 
induction  shocks  is  a  device  for  short-circuiting  auto- 


68 


INDUCTION  SHOCKS 


matically  either  the  make  shocks  or  the  break  shocks  at 
the  will  of  the  operator.  The  instrument  under  con- 
sideration lends  itself  so  readily  to  the  incorporation  of 

such  a  device  that  I  shall 
include  a  brief  descrip- 
tion of  one,  believing 
that  the  value  of  the  key 
is  enough  enhanced 
thereby  to  justify  its 
inclusion.  The  entire 
mechanism,  shown  in 
ground  plan  in  Fig.  13, 
is  mounted  upon  a  slab 
of  vulcanite,  which  in 
turn  rests  upon  a  base 
of   soapstone,   slate,   or 

other  suitable  material. 
Fig.    14.        Diagram    of    the  short-     ,^.  ,        •,      • 

circuiting    device.       t,    brass    bar,     The  Vulcamte   IS   CUt   a- 

rotating  horizontally  about  axis,    way  between  and  under- 

«     and_  bearing    mercury    cup,    0,  ^^^^^  ^j^^   :^^  ^  ^^^ 
which   IS    m    electrical    communi- 
cation with  post,  p.    s,  2',  platinum  k  ,  as  indicated  at  j  (Fig. 
pins   mounted   upon   levers,   k,  k',  13).       A      brasS      rod,      t 

(Fig.  14),  is  mounted 
upon  an  axis,  u,  in  such 
fashion  that  it  can  be  rotated  horizontally  about  this  axis 
within  the  confines  of  the  space,  5.  At  the  end  of  the  rod 
is  a  mercury  cup,  0.     Two  binding  posts,  p  and  p',  stand 


and    in    electrical    communication 
with  post,  p'. 


THE  MAKE  AND  BREAK  OF  THE  PRIMARY  CIRCUIT   69 

at  one  margin  of  the  base.  From  p  a  wire  leads  through 
the  body  of  the  vulcanite  block  to  the  rod,  /,  to  which  it 
is  soldered  near  the  axis  of  rotation  of  the  rod.  From 
p'  two  wires  are  carried  through  the  block,  one  to  the 
a.xis  of  rotation  of  the  lever,  k,  to  which  it  is  soldered,  the 
other  to  the  axis  of  k' ,  where  it  is  soldered  likewise. 
Thus  both  levers  are  in  electrical  connection  with  the 
post,  p\  and  the  rod,  /,  in  similar  connection  with  the 
post,  p.  Soldered  to  the  levers,  k  and  k' ,  at  the  points,  z 
and  z  ,  are  pins  of  platinum  projecting  downward.  These 
pins  are  so  placed  that  the  mercury  cup,  0,  can  be 
brought  directly  below  one  or  the  other  of  them  according 
as  t  is  rotated.  Their  length  is  so  adjusted  that  the  pin 
dips  into  the  mercury  when  the  lever  is  depressed  enough 
to  release  the  mechanism,  but  is  clear  of  the  mercury  at 
all  other  times. 

If  the  binding  posts,  p  and  p' ,  are  connected  in  parallel 
into  the  secondary  circuit  of  the  inductorium  and  the 
rod,  /,  is  rotated  so  as  to  bring  the  mercury  cup  below  the 
lever  which  is  pressed  when  the  primary  circuit  is  made 
(the  left-hand  one  in  this  instrument)  the  make  shocks 
are  all  short-circuited.  Bringing  the  mercury  cup  be- 
low the  other  lever  short-circuits  all  the  break  shocks. 
When  the  rod  is  placed  in  an  intermediate  position, 
neither  makes  nor  breaks  are  affected.  To  prevent  all 
possibility  of  accidental  diversion  of  the  secondary  cur- 
rent into  the  hand  of  the  operator,  vulcanite  shields  are 


70  INDUCTION  SHOCKS 

placed  on  the  levers  at  the  points  where  the  fingers  press 
upon  them,  and  upon  the  handle  by  which  the  rod,  t,  is 
rotated. 

In  addition  to  its  applicability  for  both  make  and 
break  shocks  this  key  has  the  advantage  of  preserving 
uniformity  of  action  for  a  long  time  with  little  attention. 
In  this  respect  it  is  superior  even  to  platinum  contact 
keys,  which,  as  is  well  known,  suffer  from  oxidation 
after  prolonged  use.  There  is  no  doubt,  however,  that 
well  made  automatic  platinum-contact  keys,  properly 
looked  after,  give  break  shocks  of  sufficient  uniformity 
for  the  general  purposes  of  the  physiologist. 


CHAPTER   X 

THE   INFLUENCE   OF   SECONDARY  RESISTANCE   AND    OF 
CATHODE   SURFACE 

In  the  preceding  chapters  the  scheme  for  measuring 
break  shocks  has  been  developed  to  the  point  where  it 
becomes  necessary  to  turn  from  the  induction  apparatus 
to  the  tissue  to  be  stimulated  and  to  inquire  how  varia- 
tions in  the  tissue  may  modify  stimulation  strengths. 
Two  possible  modifying  factors  have  been  indicated 
(p.  14),  as  due  to  variations  in  the  tissue;  they  are  sec- 
ondary resistance,  and  the  manner  of  applying  the  elec- 
trodes. 

The  Relation  of  Tissue  Resistance  to  Secondary  Re- 
sistance as  a  Whole.  The  secondary  circuit  usually  has 
a  comparatively  high  resistance.  Most  inductoria  used 
in  physiological  laboratories  have  secondary  coils  with 
resistances  mounting  into  hundreds  of  ohms,  and  the 
resistances  of  the  tissues  undergoing  stimulation  are 
usually  high  likewise.  In  numerous  determinations  of 
the  resistance  of  stimulated  tissues  I  have  met  with  only 
one  or  two  under  1000  ohms  and  have  found  many  ex- 
ceeding 50,000  ohms. 

Since   the   stimuli   imparted   by   faradic   currents  as 

71 


72  INDUCTION  SHOCKS 

well  as  by  those  of  galvanic  origin  arise  from  the  cath- 
ode,* and  since  the  resistance  of  the  physiological 
cathodes  must  be  small  in  comparison  with  that  of  the 
whole  mass  of  tissue  traversed  by  the  current,  we  are 
justified  in  considering  tissue  resistance  as  external  to 
the  actual  seat  of  stimulation,  and  need  make  no  dis- 
tinction between  this  and  the  other  resistances  that  may 
be  included  in  the  secondary  circuit. 

The  Method  of  Experimentation.  In  studying  the 
influence  of  secondary  resistance  experimentally  the 
usual  procedure  has  been  to  introduce  known,  non- 
inductive,  resistances  into  the  secondary  circuit  and  to 
observe  the  effect  of  their  introduction  upon  the  stimu- 
lating value  of  the  shocks  sent  through  the  circuit.  As 
a  check  upon  this  method  some  experiments  were  per- 
formed in  which  different  amounts  of  tissue  were  in- 
cluded between  the  stimulating  electrodes,  and  thus  the 
resistance  of  the  tissue  itself  was  varied.  This  latter 
method  is  of  course  less  certain  than  the  former,  since 
the  inclusion  of  more  or  less  tissue  in  the  circuit  may  mean 
a  variation  in  the  number  and  irritability  of  the  physio- 
logical cathodes  involved. 

Tissue  resistances  were  determined  by  means  of  an 
ordinary  Wheatstone  bridge  according  to  the  Kohl- 
rausch  method,  with  an  alternating  current  to  avoid 

*  Chauveau:  Journal  de  la  physiologic,  1859,  ii,  pp.  490,  553.  See 
also  Biedermann:  Elektrophysiologie,  Jena,  1895,  ii,  p.  622. 


THE   INFLUENCE   OF   SECONDARY   RESISTANCE      73 


polarization,  and  a  telephone  in  place  of  the  galvanom- 
eter. Figure  15  is  a  diagram  of  the  apparatus  required. 
The  average  of  three  readings  was  always  taken.  This 
procedure,  in  the  hands  of  one  experienced  in  its  use, 
gives  results  accurate  within  4  or  5  per  cent,  a  degree 
of  accuracy  sufficient  for  the  purposes  of  this  inquiry. 


Fig.  15.  Diagram  of  apparatus  for  measuring  tissue  resistance.  A, 
WTieatstone  bridge;  5,  telephone;  C,  small  induction  coil;  D,  battery  for 
same;  E,  key  for  same;  T,  wires  leading  to  tissue;  R,  resistance  box  con- 
nected with  switch,  S,  in  such  fashion  as  to  be  available  for  use  as 
known  resistance  of  Wheatstone  bridge,  or  as  part  of  primary  circuit,  P. 

Break  shocks  were  used  for  determining  the  threshold 

of  contraction.     The  expression  for  the  value  of  the 

M 
stimulus  is  Z,  determined  from  the  formula,  Z  =  —  I. 

The  Effect  upon  the  Stimulus  of  Varying  the  Sec- 
ondary Resistance.  The  effect  upon  the  value  of  Z  of 
varying  the  secondary  resistance  is  shown  in  two  repre- 
sentative experiments  cited  in  Table  VI.     As  appears 


74  INDUCTION  SHOCKS 

TABLE  VI 

The  Influence  of  Secondary  Resistance  upon  the  Stimulating  Values  of 
Induced  Currents 

Experiment  of  Dec.  15,  1909.  Resistance  of  Secondary  Coil  =  1400 
ohms;  of  Tissue  =  1700  ohms.  Tissue  =  Frog's  Gastrocnemius, 
Uncurarized. 

Resistance  in  secondary 

circuit 3100        6100       10,100       15,100       18,100 

Value  of  Z 496        6.81  9.45         12.45  i4-i 

Experiment  of  March  i,  19 10.  Resistance  of  Secondary  Coil  =  1400 
ohms;  of  Tissue  =  16,600.  Tissue  =  Frog's  Sartorius,  Uncura- 
rized. 

Resistance  in  secondary  circuit . .  18,000  28,000  48,000  68,000 
Value  of  Z 3.97  5.24  6.8  9 

from  this  table,  stronger  stimuli  are  required  to  produce 
a  given  physiological  effect  when  the  secondary  resist- 
ance is  high  than  when  it  is  low.  That  there  is  a  defi- 
nite mathematical  relationship  between  the  effective- 
ness of  the  stimulus  and  the  secondary  resistance  is 
shown  by  plotting  these  values  as  a  curve.  Such  a 
curve  for  the  first  experiment  of  Table  VI  is  given  in 
Fig.  16.  It  is  virtually  a  straight  line  having  the  gen- 
eral equation 

^(R  +  A) 
2  =  ^ « 

in  which  Z  is  the  intensity  of  the  shock  required  at  re- 
sistance R  to  produce  the  desired  effect,  and  ^  and  A 


THE   INFLUENCE   OF   SECONDARY   RESISTANCE      75 

are  constants.  This  fomiula  has  been  found  to  hold 
in  all  of  the  several  hundred  experiments,  in  which  it 
has  been  applied.     The  value  of  the  constant  /3  in  any 


12 


10 


yo: 


4000 


aooo 


i:Jooo 


luooo     20000 


Fig.  16.  Sho\\ing  that  the  curve  of  increasing  stimulus  against 
increasing  resistance  is  a  straight  line.  Abscissae  represent  values  of  Z; 
ordinatcs  represent  resistances  in  ohms. 


given  experiment  can  be  determined  geometrically  by 
producing  the  curve  to  where  it  cuts  the  ordinate  for 
zero  resistance.     According  to  Fig.   16,  the  value  of  /3 


76  INDUCTION  SHOCKS 

for  the  experiment  of  Table  VI  from  which  that  curve  is 
derived  is  3.  Since  this  represents  the  value  of  Z,  whose 
effect  at  zero  resistance  would  equal  that  of  the  various 
other  values  of  Z  at  their  respective  resistances,  it 
affords  a  measure  of  the  irritability  of  the  physiological 
cathode  where  the  stimulus  actually  arose,  on  the  as- 
sumption that  the  resistance  of  the  cathode  is  negligibly 
small.  We  have,  therefore,  in  j3  an  expression  for  the 
value  of  any  stimulus  as  it  affects  the  seat  of  actual 
stimulation,  namely,  the  physiological  cathode,  irre- 
spective of  the  resistance  of  the  secondary  circuit. 

By  a  slight  transposition  of  equation  (i)  the  equation 
for  (3  becomes : 

/3  = »  (2) 

^      R+A  ^ ^ 

and  if  the  value  of  Z  for  any  secondary  resistance  is 
known,  the  actual  or  "specific"  stimulus  can  be  calcu- 
lated from  equation  (2),  provided  only  the  value  of  the 
other  constant,  A,  is  known.  For  measuring  stimuli 
with  reference  to  the  resistance  through  which  they  are 
apphed  there  must  be  added  to  the  determinations 
previously  required,  therefore,  not  only  the  secondary 
resistance,  but  a  constant  A. 

Current  Density  an  Important  Factor.  That  the  stim- 
ulating effectiveness  of  electric  currents  varies  with  their 
density  has  long  been  recognized,*  although  practical 

*  Biedermann:  Loc.  cit.,  i,  p.  185. 


THE   INFLUENCE   OF  SECONDARY   RESISTANCE      77 

application  of  the  fact  has  hitherto  been  reserved  for 
galvanic  stimulation.  The  expression  for  /3  shows  that 
current  density  is  a  factor  to  be  taken  into  account  in 
measuring  faradic  stimuli  as  well. 

_,     ,  .  .      ,  .  Z^ 

The  factor  A  m  the  expression  /3  =  -  —  is  the  pro- 
vision by  which  allowance  is  made  for  the  influence  of 
current  density.  The  stimulating  efTectiveness  of  dense 
currents  is  greater  than  of  diffuse  ones.  In  order  that 
the  expression  for  jS  agree  with  this  fact  the  value  of  A 
must  increase  as  the  density  of  the  stimulating  current 
increases.  Experimental  evidence  showing  that  A  is 
actually  larger  for  dense  currents  than  for  diffuse  cur- 
rents is  contained  in  an  experiment  cited  on  p.  109, 
Chap.  XII. 

I  do  not  know  of  any  reliable  method  of  determining 
the  value  of  the  constant.  A,  other  than  that  used  in 
this  work,  namely  to  estabHsh  experimentally  tw^o  or 
more  values  of  Z  for  different  secondary  resistances, 
and  from  these  values  compute  the  value  of  A.  This 
can  be  done  by  means  of  the  equation 

ZrR'  —  Zr'R 
^  =  -7 7—'  (3) 

^R'  ~  ^R 

in  which  Zr  and  Zr>  are  the  stimuli  required,  with  re- 
sistances R  and  R'  respectively,  to  produce  the  minimal 
contractions  used  as  the  index. 


78  INDUCTION  SHOCKS 

The  Dependence  of  Factor  A  upon  Inductorium  Con- 
struction. In  discussing  the  method  of  comparing  one 
inductorium  with  another  by  the  introduction  of  the 

MI 
factor  L  in  the  expression  Z  =  — —  >  it  was  stated  (p.  52) 

that  this  comparison  is  subject  to  a  certain  restriction  as 
to  secondary  resistance.  This  restriction  rests  upon  an 
observation  of  Gildemeister,*  according  to  which,  if  two 
dissimilar  inductoria  are  compared  quantitatively  by  the 
method  outlined  here,  in  which  the  expression  for  the 

M  .      . 

value  of  a  stimulus  is  Z  =  —  X  /,  it  will  be  found  that 

although  equal  stimuli  may  yield  corresponding  values 
of  Z  from  the  two  inductoria,  with  certain  secondary 
resistances,  when  other  secondary  resistances  are  used 
equal  stimuli  will  not  give  corresponding  values  of  Z. 

In  earlier  paragraphs  of  this  chapter  it  was  pointed 
out  that  the  true  or  specific  value  of  a  stimulus  is  not 
afforded  by  the  expression  Z,  but  by  the  expression  /3, 
which  depends  not  only  upon  Z  but  upon  the  secondary 
resistance  and  a  constant  A  as  well.  The  determination 
of  ^,  as  previously  shown,  is  according  to  the  formula 

ZrR'  —  Zr'R 
A  =-y y—' 

^R'  —  ^R 

in  which  Z^  and  Zji>  are  stimuli  which,  with  resistances 

*  Gildemeister:  Archiv  fiir  die  ges.  Physiologic,  1910,  Bd.  131, 
S.  604. 


THK    INFLUENCE  OF   SECONDARY   RESISTANCE      79 

R  and  R'  rcsix'ctivcly,  have  equal  physiological  effect. 
Since  dissimilar  inductoria  fail  to  give  corresponding 
values  of  Z  at  all  secondary  resistances,  the  value  of  A 
determined  by  this  formula  from  one  inductorium  will 
not  necessarily  agree  with  its  value  as  obtained  from 
another.  The  value  of  A,  therefore,  does  not  depend 
solely  upon  the  surface  of  the  physiological  cathodes, 
but  in  part  also  upon  the  construction  of  the  inducto- 
rium. 

This  variation  in  the  values  of  A  determined  from  dis- 
similar inductoria,  which  might  lead  one  to  question  the 
validity  of  the  equation  in  which  A   is  employed,  i.e., 

ZA 

/3  =  — 7 '  serves  in  fact  to  confirm  strongly  the  valid- 

R  -h  A 

ity  of  that  equation  and  the  use  of  the  expression  jS  to 
signify  the  specific  value  of  the  stimulus.  This  con- 
firmation rests  upon  the  repeated  observation  that  when 
equal  stimuli  are  generated  by  dissimilar  inductoria  the 
values  of  /3  are  equal  even  though  the  observed  values  of 
Z  and  the  computed  values  of  A  may  be  quite  divergent. 
An  experiment  illustrating  this  point  is  summarized  in 
Table  VII.  Details  of  the  construction  of  the  induc- 
toria used  are  given  in  Table  \TII.  The  experiment 
shows  that  dissimilar  inductoria  give  for  equal  break 
stimuli  perfectly  concordant  values  if  all  the  factors 
which  make  up  the  final  expression  for  stimulation 
strength  arc  taken  into  account. 


8o 


INDUCTION  SHOCKS 


TABLE  VII 

Demonstrating   that  Equal   Stimuli  give  Equal  Values  of  /S  in 

ZA 
the  Equation  /3  =  „        .  >  when  the  Stimuli  are  generated  by 

Dissimilar  Inductoria 


Inductorium. 


First  sec.  resistance..  . 

First  Z 

Second  sec.  resistance. 

Second  Z 

Calculated  A 

Calculated  j3 


H. 


8,850  ohms 

0.76 
25,500  ohms 
1 .60 

6,200 
0.31 


9,000  ohms 

0.604 
25,600  ohms 
1. 18 
8,400 
0.292 


9,800  ohms 
0.588 

26,400  ohms 
1.06 

10,800 

0.308 


The  differences  in  secondary  resistance  in  corresponding  columns  are 
due  to  the  different  resistances  of  the  secondary  coils,  it  being  necessary 
to  include  these  resistances  as  part  of  the  secondary  circuit. 


TABLE   VIII 
Details  of  Construction  of  the  Inductoria  used  in  this  Study 


Coil. 

Length  of 
secondary. 

Turns  in  sec- 
ondary. 

Resistance 
of  second- 
ary. 

Remarks. 

A 
B 

G 

E 
H 

N 

cm. 
12.5 

13.0 

13.0 

6.5 
9-3 
9-3 

10,000 

10,350 

10,260 

5,000 
6,000 
8,000 

850 
1400 

770 

300 
450 
600 

(  Kronecker 
(    graduation 
(  Kronecker 
(    graduation 
j  Kronecker 
1    graduation 
Porter  inductorium 

Conditions  in  which  the  Specific  Stimulus  need  not 

ZA 


be  determined.    While  we  have  in  the  formula  /3 


R-\-A 


THE  INFLUENCE  OF   SECOND.VRY   RESISTANCE       8l 

a  means  of  expressing  the  specific  value  of  any  break  in- 
duction shock,  no  matter  how  the  factors  concerned  in 
its  production  may  var>',  we  must  recognize  that  in  the 
ordinary  practice  of  the  physiologist  the  attempt  to 
make  use  of  this  formula  presents  very  considerable 
difficulties.  These  difficulties,  moreover,  are  chiefly  in 
connection  with  the  inclusion  of  the  factors  R  and  A, 
and  we  may  well  inquire  how  great  errors  are  likely  to 
arise  in  comparing  faradic  stimuli  if  these  two  factors 
are  completely  disregarded. 

We  must  reahze  at  the  outset  of  this  part  of  our  in- 
quiry that  if  comparisons  are  attempted  between  stimuli 
used  under  conditions  of  widely  varying  secondary  re- 
sistance and  divergent  cathode  surface,  disregard  of 
these  two  factors  is  sure  to  lead  to  erroneous  conclu- 
sions; but  probably  in  a  majority  of  physiological 
experiments  the  stimuh  to  be  compared  are  produced 
under  conditions  which  tend  to  be  closely  similar.  With 
regard  to  such  cases  as  these  we  may  properly  inquire 
whether  the  factors  under  consideration  need  be  taken 
into  account. 

Successive  Stimulation  of  the  Same  Tissue.  Prob- 
ably the  experiments  in  which  accurate  comparisons  of 
stimuli  are  most  needed  are  those  in  which  a  given 
tissue  is  to  be  stimulated  successively.  But  in  experi- 
ments of  this  class  neither  the  tissue  resistance  nor  the 
electrode  surfaces  undergo  noteworthy  variation  during 


82  INDUCTION  SHOCKS 

the  course  of  the  experiment  and  so  do  not  enter  as 
modifying  factors. 

Stimulation  of  Corresponding  Tissues  in  Different 
Animals.  Next  in  importance  are  cases  in  which  it  is 
desired  to  impart  comparable  stimuli  to  corresponding 
tissues  through  a  series  of  experiments.  Cases  of  this 
sort  arise  frequently  in  the  course  of  physiological  re- 
search, and  I  have  therefore  given  them  special  consid- 
eration. 

While  this  subject  was  before  me  there  was  being  car- 
ried on  in  the  laboratory  at  Harvard  an  investigation 
which  involved,  among  other  things,  determining  in  a 
series  of  cats  the  threshold  stimulus  for  producing  ex- 
tension of  the  wrist,  when  the  stimulus  was  applied  to 
the  deep  branch  of  the  radial  nerve  below  the  elbow; 
and  reflex  flexion  of  the  hind  leg  through  stimulation  of 
the  tibial.  Here  was  presented  a  typical  example  of  the 
class  of  experiments  described  in  the  paragraph  heading, 
and  I  therefore  utilized  it  in  the  study  of  my  problem. 
In  several  cases  the  threshold  stimulus  was  determined 
when  the  tissue  only  was  in  the  secondary  circuit,  and 
immediately  afterward,  the  threshold  when  an  additional 
resistance  of  10,000  ohms  had  been  introduced.  I  was 
thus  able  in  these  cases  to  compute  the  value  of  the  con- 
stant A ,  and  from  it  to  obtain  the  solution  of  the  equa- 

ZA 

tion  for  "specific"  irritabiHty,  /3  =  — j-      In  the  ex- 

R  -\-  A 


THE   INFLUENCE  OF   SECONDARY   RESISTANCE      83 

pcrimcnts  of  this  scries,  ten  in  all,  the  secondar}-  re- 
sistances ranged  from  2800  ohms  to  6000  ohms,  averag- 
ing 3900  ohms.  The  values  of  A  ranged  from  4300  to 
14,000,  averaging  7800.  The  statistics  for  this  series 
are  given  in  Table  IX. 


TABLE  IX 

Illustrating  the  Tendency  of  /3  and  Z  to  vary  similarly  in  Direc- 
tion and  Extent.  Z  represents  the  Stimulus  producing  Just 
Perceptible  Wrist  Extension  in  Cat.  Stimulus  applied  to 
Deep  Branch  of  Radial  Nerve 

Ratio 
Date.ipio.  ?,ff°ff-7     Value  of  .4.     ^fT       IV^"        |. 


Aug.  8. 
July  28 
Aug.  5. 
Aug.  3. 
Aug.  9. 
Aug.  2. 
Aug.  17 


Secondary 
resistance. 

Value  of  .4. 

Value 
of  Z. 

Value 
of;3. 

6000 

7500 

2.77 

1-54 

4400 

5000 

3    19 

1-7 

4800 

8000 

3-84 

2.4 

3400 

7800 

4.32 

30 

3000 

9800 

552 

4.22 

4600 

9600 

6.05 

4.08 

2800 

4600 

254 

iS-8 

■S6 
■53 
.62 
.70 

•  77 
.68 
.62 


As  Above  except  that  Stimulus  was  applied  to  Tibial  Nerve,  and 
Reflex  Flexion  of  Hind  Leg  was  Movement  Evoked 


July  18 

July  22 

July  20 

Average. 


3000 
4000 
3000 


4.300 

14,000 

7,000 


4.08 
6.6 
24.7 


2-4 

17-3 


•59 
•77 
.70 

.65 


Inspection  of  the  tabic  reveals  a  definite  tendency  of 
(3  to  vary  as  does  Z.  The  closeness  of  this  tendency  is 
brought  out  more  strikingly,  however,  in  Fig.    17,  in 


84 


INDUCTION   SHOCKS 


which  the  ratios  of  ,8  to  Z  in  successive  experiments  are 
plotted.  The  horizontal  line  represents  the  average 
ratio  of  iS  to  Z  as  determined  in  these  experiments;  the 
variations  from  this  line  of  the  different  actual  ratios 
are,  as  is  seen,  relatively  inconsiderable,  the  greatest 
being  18.5  per  cent,  the  average  of  all  slightly  under 
II  per  cent. 

Assuming  the  data  cited  in  Table  IX  to  be  fairly  Tep- 
resentative  of  the  relations  between  /3  and  Z  that  are 


1.0 

, , 

' — =, 

,  ^ 

( ^ 

0.5 

' 

i ^ 

^       "^ 

*^      -^ 

>-• 

Exp.  1 


10 


Fig.  17.  Illustrating  the  relatively  slight  departures  of  individual 
ratios  of  j8  to  Z  from  the  average.  Ordinates  represent  successive  ex- 
periments; abscissas  represent  ratios  of  ^  to  Z.  The  horizontal  Une 
is  drawn  at  the  level  of  the  average  ratio. 


likely  to  occur  in  experiments  of  the  sort  under  consid- 
eration, to  what  extent  are  we  justified  in  such  experi- 
ments in  making  use  of  the  values  of  Z  for  expressing 
quantitative  relationships? 

The  figures  show  clearly,  I  think,  that  all  except  the 
finest  relationships  are  revealed  with  sufficient  exactness 
by  the  values  of  Z.  While  one  cannot  always  know  cer- 
tainly, in  cases  in  which  several  nearly  equal  values  of 
Z  are  under  comparison,  which  will  give  smaller  and 


THE  INFLUENCE  OF   SECONDARY   RESISTANCE      8$ 

which  larger  values  of  /3,  yet,  if  the  experiments  are 
carefully  performed,  one  can  be  practically  certain, 
whenever  the  values  of  Z  dififer  by  more  than  15  or  18 
per  cent,  that  the  larger  Z  means  also  a  larger  /3.  With 
this  degree  of  accuracy  assured,  probably  the  demands 
of  most  researches  of  this  class  are  fully  met,  and  all 
such  may  safely  disregard  both  the  secondary  resistance 
and  the  cathode  surfaces. 

Differing  from  the  series  of  experiments  quoted  above 
in  that  they  offer  wider  variations  in  both  secondary 
resistance  and  electrode  surface,  and  therefore  greater 
likeUhood  of  error  if  these  factors  be  disregarded,  is  a 
series  of  obser\^ations  on  frogs'  gastrocnemius  muscles, 
carried  out  by  myself. 

In  the  series  of  eighteen  experiments  cited  in  Table  X 
the  secondary  resistances  ranged  from  3100  to  13,000 
and  the  values  of  A  from  2600  to  13,500.  Yet,  in  spite 
of  these  wide  ranges  in  the  values  of  the  factors  deter- 
mining the  relation  of  Z  to  fi,  this  latter  relation  varies 
to  a  surprisingly  moderate  degree.  The  average  ratio 
of  /3  to  Z  is  .49.  The  widest  departures  from  this  are 
ratios  of  .32  and  .64,  amounting  to  35  per  cent  and  31 
per  cent  respectively,  while  the  average  variation  is  only 
15  per  cent.  If  the  experiments  of  Table  X  represent 
fairly  the  variations  in  secondary  resistance  and  cathode 
surface  Ukely  to  be  met  with  in  experiments  on  frogs' 
gastrocnemii,  we  can  safely  conclude  that  the  values  of 


86 


INDUCTION  SHOCKS 


Z,  obtained  in  any  such  experiment,  represent  the  true 
relative  values  of  the  stimuli  used  within  one-third. 


TABLE   X 

Illustrating  Tendency  of  Z  and  /3  to  vary  together, 
trocnemii  stimulated  directly 


Frogs'  Gas- 


Date. 


Secondary 
resistance. 


Value  of  A . 


Value 
ofZ. 


Value 
of/3. 


Ratio 
Z' 


Feb. 

Oct. 

Dec. 

Jan. 

Feb. 

Feb. 

Feb. 

Jan. 

Mar. 

Feb. 

Nov. 

Feb. 

Jan. 

Dec. 

Jan. 

Feb. 

Feb. 

Nov, 


24,  1910. . . 
28,  1909. . . 
15,  1909.., 
19,  1910.  . . 

17,  1910. . . 
24,  1910. . . 

18,  1910. . . 
31,  1910  . . 

7,  1910 

18,  1910 
,  18,  1909. . 

10,  1910. . . 
31,  1910. . . 

13,  1909.. 
31,  1910.  . . 

18,  1910. . . 

17,  1910. . . 

.  4,  1909.  .  . 

Average . 


5. 400 
6,500 
3,100 
8,400 
6,800 
6,400 
S.ooo 
11,400 
5,400 

5-Soo 
7,700 
13,000 
10,400 
5,000 
6,200 
5,000 
6,000 
3,200 


6,900 
6,000 
5, 000 
4,800 
7,500 
4,200 
4,800 

13,500 
4,800 
5,500 
4,200 
6,000 
9,000 
5,000 

10,500 
4,800 

10,500 
2,600 


6. 12 
6.  24 
II. 9 
12.2 

12.35 

12.5 

12.7 

12.95 

14.6 

14.6 

1535 
16.8 
19.  2 
19.9 
22 . 1 
22.8 
24.7 
41-5 


3-4 

30 

7-35 

4-45 

6.5 

4-95 

6.2 

7.0 

6.86 

7-3 

5 -40 

5-30 

8.90 

9.96 


•56 
.48 
.62 
•36 
•52 
.40 

■49 
•54 
•47 
•SO 
•35 
•32 
•  46 
•5° 
•63 
•49 
.64 
•45 
•49 


In  a  series  of  ten  experiments  on  frogs'  gastrocnemii 
stimulated  through  the  sciatic,  with  resistances  ranging 
from  6300  to  38,000  ohms,  and  values  of  A  from  6000  to 
23,000,  the  ratio  of  jS  to  Z  averaged  .48,  and  the  widest 
variation  was  a  ratio  of  .28,  amounting  to  42  per  cent, 
the  average  variation  being  20  per  cent.  In  the  experi- 
ments cited  in  the  two  series  above  no  attempt  was 


THE  INFLUENCE  01"   SECOXDAKV   RESISTANCE      87 

made  to  keep  conditions  of  tissue  resistance  and  cathode 
surface  approximately  uniform.  On  the  contrary,  these 
conditions  were  purposely  made  to  vary  widely  from  one 
experiment  to  another.  I  feel,  therefore,  that  they  cover 
the  range  of  variation  likely  to  occur  in  ordinary  experi- 
mentation. 

These  data  seem  to  me  to  show  that  in  the  hands  of 
a  careful  experimenter,  who  will  take  pains  to  keep  his 
conditions  of  stimulation  as  uniform  as  possible,  quanti- 
tative results  of  great  value  may  be  obtained  without  the 
labor  involved  in  taking  account  of  secondary  resistance 
and  cathode  surface.  By  the  use  of  the  method  out- 
Hned  in  previous  chapters  the  strengths  of  stimuli  em- 
ployed in  any  given  case  may  be  expressed  in  terms  of 
stimulation  units,  and  if  the  conditions  of  experimenta- 
tion, such  as  the  nature  of  electrodes  used,  distance  be- 
tween them,  and  method  of  applying  them,  are  carefully 
described,  other  experimenters  can  duplicate  the  stimuli 
very  closely.  Certainly  this  method  allows  comparisons 
of  much  greater  accuracy  than  can  be  made  by  the  ex- 
isting methods  of  describing  stimuli.  It  is  highly  im- 
portant, however,  that  investigators  attempting  to  use 
induction  shocks  quantitatively  recognize  fully  the  limi- 
tations upon  accuracy  which  are  involved  in  disregard- 
ing the  factors  under  discussion.  So  long  as  there  is  no 
effort  to  draw  conclusions  which  are  not  warranted  by 
the  degree  of  accuracy  actually  obtained,  no  harm  will 


88  INDUCTION  SHOCKS 

be  done,  but  wherever  the  occasion  exists  for  a  high 
degree  of  accuracy  in  determining  stimuU,  secondary  re- 
sistance and  cathode  surface  must  be  taken  into  account. 

A  Standard  of  Inductorium  Construction  Necessary. 
In  connection  with  this  discussion  of  the  circumstances 
in  which  the  factors  of  secondary  resistance  and  cathode 
surface  may  be  disregarded,  we  must  not  forget  that  the 
structure  of  the  inductorium  is  interwoven  with  the 
factor  of  cathode  surface  (see  p.  78),  in  such  fashion 
that  the  latter  cannot  be  left  out  of  account  without 
error  unless  the  former  has  been  provided  for.  This  pro- 
vision is  best  made  by  adopting  a  standard  of  inducto- 
rium construction  and  using  for  quantitative  purposes 
only  instruments  conforming  reasonably  to  it.  Thus  we 
become  at  once  independent  of  inductorium  structure 
as  a  complicating  factor,  and  are  free  to  measure  stimuli 
in  many  cases  in  the  simpler  manner  discussed  above. 

The  desirability  of  having  a  standard  of  inductorium 
construction  for  physiological  and  clinical  use  was  recog- 
nized fully  thirty  years  ago.  In  an  attempt  to  establish 
one  the  Paris  Electrical  Congress  of  1881  resolved  at  its 
session  of  September  28th  that  the  form  of  inductorium 
at  that  time  in  use  in  the  University  of  Berlin  should  be 
adopted  as  the  standard.* 

*  See  Lewandowski:  Elektrodiagnostik  und  Elektrotherapie,  Wien 
und  Leipzig,  1887,  S.  212.  Also  Hoorweg:  Die  medicinische  Elektro- 
technik  und  ihre  physikalischen  Grundlagen,  Leipzig,  1893,  S.  128. 


THE  IXFLUENCE  OF  SECONDARY   RESISTANCE      89 

The  dimensions  of  that  inductorium  are  as  fol- 
lows: 

Primary  Secondary 

Length  of  coil 88  mm.  65  mm. 

Diameter  of  coil 36  mm.  68  mm. 

Diameter  of  wire i  mm.             0.25  mm. 

Number  of  turns  of  wire 300  5000 

Number  of  layers  of  wire 4  28 

Resistance 1.5  ohms  300  ohms 

Unfortunately  for  the  general  acceptance  of  these 
dimensions  as  standard,  Kronecker  *  had,  ten  years  ear- 
lier, proposed  his  well-known  system  of  units,  based  on 
determinations  made  with  inductoria  having  coils  twice 
as  long  as  the  Berlin  coils  and  each  with  twice  as  many 
turns  of  wire;  and  with  the  adoption  of  his  graduation 
the  large  coils  came  into  common  use.  By  general  con- 
sent among  physiologists,  therefore,  rather  than  by  any 
official  action,  inductoria  having  coils  about  13  cm.  long 
and  having  about  10,000  turns  in  the  secondary  are 
recognized  as  suitable  for  the  uses  of  the  investigator. 
In  most  well-equipped  laboratories  such  inductoria  are 
found,  and  there  seems  no  valid  reason  why  the  general 
dimensions  originally  selected  by  Kronecker  for  his  grad- 
uation should  not  be  taken  as  standard.  In  a  later  para- 
graph (p.  92),  observations  will  be  cited  which  show 
that  for  quantitative  work  coils  of  this  size  are  to  be  pre- 

*  Kronecker:  Arbeiten  aus  der  physiologischen  Anstalt  zu  Leipzig, 
1871,  S.  186. 


90  INDUCTION  SHOCKS 

ferred  to  the  smaller  ones  recommended  by  the  Paris 
Congress. 

Assuming  as  the  standard,  then,  an  inductorium  hav- 
ing coils  about  13  cm.  long  and  having  in  the  secondary 
approximately  10,000  turns  of  wire,  we  may  inquire 
how  widely  an  inductorium  can  vary  from  this  standard 
without  introducing  a  significant  error.  For  answering 
this  question  I  have  made  observations  with  six  in- 
ductoria,  three  of  which  are  of  "standard"  construction 
and  provided  with  Kronecker  graduations,  the  other 
three  selected  to  give  increasing  degrees  of  divergence 
from  the  standard.  Details  of  the  construction  of  the 
six  inductoria  are  set  down  in  Table  VIII. 

The  results  of  my  numerous  experiments  with  these 
inductoria  may  be  summarized  as  follows:  The  three 
standard  coils,  A,  B,  and  G,  give  corresponding  values 
of  Z  for  equal  stimuH  and  equal  secondary  resistances 
whatever  the  secondary  resistance  may  be.  In  compar- 
ing them,  therefore,  the  factor  of  inductorium  construc- 
tion does  not  enter. 

In  thirteen  experiments  in  which  coil  N  was  compared 
with  coil  B  the  secondary  resistances  ranged  between 
2850  ohms  and  25,000  ohms;  the  average  percentage 
variation  of  Z^*  from  Zb  was  6  per  cent;  the  greatest 
variation  was  11. 6  per  cent.     Z^  was  greater  than  Zb 

*  For  convenience  of  expression  a  subscript  is  placed  after  the  value 
of  Z  to  indicate  with  which  coil  the  value  was  obtained. 


THE   INFLUENCE   01"   SECONDARY    RESISTANCE      91 

four  times  and  Zb  greater  than  Z^  nine  times.  The 
small  average  percentage  diflerence  between  the  two 
coils,  a  difference  only  slightly  greater  than  the  probable 
experimental  error,  coupled  with  the  fact  that  not  all  the 
variations  are  in  the  same  direction,  seems  to  me  to 
show  that  in  coils  differing  no  more  than  these  the  in- 
fluence of  inductorium  construction  as  a  special  factor 
can  be  disregarded  without  serious  error. 

An  important  effect  of  inductorium  construction  be- 
comes manifest  when  coils  B  and  H  are  compared.  The 
average  difference  between  Zb  and  Z^i  in  twelve  experi- 
ments was  16  per  cent;  in  four  of  the  twelve  cases,  more- 
over, the  difference  exceeded  24  per  cent.  Analyzing  the 
series  of  experiments  with  reference  to  the  secondary  re- 
sistances it  appeared  that  the  high  average  difference  is 
due  to  large  differences  in  the  experiments  with  high  sec- 
ondary resistance.  Thus  five  experiments  with  second- 
ary resistance  above  10,000  ohms  show  an  average  differ- 
ence between  Zb  and  Z//  of  25.7  per  cent,  while  seven 
experiments  with  secondary  resistances  below  10,000 
ohms  show  an  average  difference  of  only  4.5  per  cent. 
In  all  five  experiments  with  high  secondary  resistance 
Zfj  was  greater  than  Zb-  In  the  seven  experiments  with 
low  resistance  Z//  was  larger  than  Zb  three  times,  smaller 
than  Zb  twice,  and  equal  to  it  twice. 

This  series  of  experiments  shows  that  in  inductoria 
differing  even  so  widely  as  do  coils  B  and  H,  inducto- 


92 


INDUCTION  SHOCKS 


rium  construction  is  unimportant  so  long  as  secondary 
resistance  is  kept  low.  It  is,  however,  of  great  impor- 
tance whenever  the  secondary  resistance  is  high. 

The  final  series  of  comparisons  was  between  coil  B 
and  the  Porter  inductorium,  coil  E.  This  yielded  re- 
sults of  the  same  sort  as  the  preceding  comparison,  but 
more  marked.  Only  with  very  low  secondary  resistances 
were  Zb  and  Z^  equal,  and  Ze  became  relatively  more 
and  more  in  excess  of  Zb  as  the  secondary  resistance  was 
increased.  Table  XI  illustrates  this  relationship  very 
clearly. 

This  last  experiment  brings  out  clearly  the  objection 
to   the  standard  set  by  the   Paris   Congress  of   1881 


TABLE  XI 
Illustrating  the  Increasing  Divergence  of  Z^  from  Z^  with  In- 
creasing Secondary  Resistance 


Resistance  in  sec- 
ondary circuit. 

Zj,. 

Ze- 

Percentage 
variation  of 
Z^  from  Z^. 

900  ohms 

1,600  ohms 

2,700  ohms 

8,600  ohms 

20,600  ohms 

15-75 

17.9 

18.7 

24.1 

49.0 

16.05 
19.8 
26.8 
46.0 
135-0 

1-9 

10.6 

43  0 

91.0 

I7S-0 

(p.  89).  The  Porter  inductoria  conform  closely  to  that 
standard  in  all  respects  save  that  of  diameter  of  the  coils. 
As  Table  XI  shows,  the  influence  of  secondary  resistance 
upon  stimulating  value  is  very  much  more  marked  in 


THE  INFLUENCE  OF  SECONDARY   RESISTANCE      93 

the  small  inductorium  than  in  the  larger  one,  so  that 
while  there  are  many  sorts  of  experiments  in  which  the 
investigator  using  a  large  coil  is  justified  in  disregarding 
secondary  resistance,  to  do  so  would  nearly  always  be 
unsafe  if  a  small  coil  were  being  employed.* 

*  The  Porter  inductorium  with  which  this  experiment  was  per- 
formed is  of  the  old,  or  student,  tjpe.  The  new  form,  which  is 
constructed  in  accordance  with  the  Kronecker  specifications,  is  well 
adapted  for  quantitative  work. 


CHAPTER  XI 
THE  MEASUREMENT   OF  MAKE   SHOCKS 

In  order  that  the  scheme  for  making  induction  shocks 
quantitatively  useful  may  be  complete,  a  method  for 
measuring  make  shocks  must  be  added  to  the  one  already 
developed  for  break  shocks.  The  method  to  be  pre- 
sented in  this  chapter  is  based  wholly  on  experimental 
comparisons  between  make  shocks  and  break  shocks 
by  the  v.  Fleischl  method  previously  described  (p.  56). 
That  it  is  valid  can  scarcely  be  doubted  in  view  of  the 
large  number  of  concordant  experiments  which  support 
it.* 

The  expression  for  make  shocks  should,  of  course,  be 

directly  comparable  with  the  one  previously  developed 

for  break  shocks.     The  factors  of  secondary  resistance 

and  cathode  surface  affect  makes  and  breaks  alike.     We 

may  take  as  a  starting  point  from  which  to  develop  a 

formula  for  make  shocks,  therefore,  the  expression  for 

break  shocks  which  takes  account  of  neither  of  these 

MI 
factors,  namely  Z  =  — -•      The  problem  to  be  solved  is 

how  this  expression  must  be  modified  so  that  the  value 

*  Martin:  Am.  Jour,  of  Physiology,  1909,  xxiv,  p.  276  et  seq. 
94 


THE  MEASUREMENT  OF  MAKE  SHOCKS     95 

Z  as  applied  to  make  shocks  shall  represent  stimuli 
equal  in  intensity  to  those  given  by  break  shocks  in 
which  the  value  of  Z  is  determined  as  above.  The  ex- 
perimental procedure  by  which  the  problem  was  solved 
was  as  follows:  A  series  of  equal  make  stimuli  were 
obtained  with  the  secondary  coil  at  various  distances 
from  the  primary.  The  "caUbration  number"  for  each 
secondary  position  was  then  multiphed  by  the  intensity 
of  primary  current  employed  at  that  position,  and  the 
products  for  each  experiment  were  set  down  in  a  table.* 
For  the  inner  positions  of  the  secondary  coil,  positions 

which  have  relatively  large  values  of  ^.  the  product 

— -  X  /  was  nearly  constant;   as  the  secondary  coil  was 

moved  out  into  the  parts  of  the  field  where  the  values 

of  —are  small,  the  product  "i^  X  /  became  progressively 

larger  the  farther  out  the  secondary  coil  was  pushed,  and 

consequently  the  smaller  were  the  values  of  —  •     Nu- 

merous  repetitions  of  the  experiment  gave  precisely  sim- 
ilar results. 

These  experiments  indicated  quite  clearly  the  exist- 
ence of  a  comparatively  simple  relationship  between 
make  and  break  stimuU,  and  also  suggested  a  method 

*  For  experimental  data  see  Martin:  hoc.  cit.,  p.  272. 


96  INDUCTION  SHOCKS 

for  expressing  the  relationship  mathematically  in  the 
simplest  possible  fashion,  namely  through  the  introduc- 
tion of  a  single  factor  into  the  break  shock  formula, 
which  when  introduced  would  cause  it  to  give  equal 
values  for  Z  for  equal  make  stimuli.  Study  of  the 
data  showed  that  the  factor  to  be  introduced  must  be 

M 

relatively  larger  the  smaller  the  value  of  — ,  and  must 

M 
tend  to  diminish  —  •     A  constant  number  has  this  effect 

M 
if  it  is  subtracted  from  —  •     The  formula  modified  in 

accordance  with  this  idea  becomes 
Z 


=  (f -.)/.*  « 


In  practically  every  experiment  of  a  large  series  some 
number  could  be  selected  to  be  substituted  for  K  in 
formula  (i)  with  a  fairly  constant  value  of  Z  resulting. 
For  each  experiment  the  value  of  K  had  to  be  deter- 
mined empirically,  and  it  varied  widely  in  different  ex- 
periments.    In  all  the  experiments  the  values  of  K  were 

...  M 

neghgibly  small  m  comparison  with  the  values  of  —  for 

secondary  positions  of  12  cm.  or  less. 

The  discovery  of  the  above  formula  is  a  decided  step 
toward  the  ultimate  solution  of  the  problem  of  measur- 

*  To  distinguish  between  break  stimuli  and  make  stimuli  the  former 
are  represented  by  Zh,  the  latter  by  Zm- 


THE   MEASUREMENT  OF   MAKE   SHOCKS  97 

ing  make  shocks,  but  it  is  not  a  complete  solution,  since 
it  offers  no  means  of  determining  in  advance  what  the 
value  of  A'  will  be  under  any  given  set  of  conditions. 
The  next  step  was  to  study  a  large  series  of  experiments 
with  reference  to  the  conditions  upon  which  the  values 
of  K  depend. 

It  became  apparent  at  an  early  stage  of  the  investi- 
gation that  make  shocks,  unlike  breaks,  are  modified  in 
intensity  by  changes  in  the  voltage  of  the  primary  cur- 
rent. This  observation  suggested  the  grouping  of  all 
the  experiments  according  to  the  primary  voltage  used 
in  performing  them.  After  this  had  been  done  the 
values  of  K  for  the  different  experiments  of  any  group 
still  differed  widely,  but  now  wherever  the  value  of  K 
was  large  the  value  of  Z  was  also  large  and  vice  versa. 
This  suggested  at  once  a  possible  dependence  of  the 
value  of  K  upon  that  of  Z.  To  test  this  possibility  the 
experiments  of  each  group  were  plotted,  values  of  K 
against  values  of  Z.  The  resulting  curve  in  each  case  is 
a  straight  line,  having  the  simple  equation 

K  =  aZ.  (2) 

Fig.  18  gives  the  curve  for  coil  B  obtained  by  plotting 
the  experiments  at  2  volts.  The  value  of  a  given  by 
this  curve  is  18.  Substituting  in  equation  (i)  the  value 
of  K  given  in  equation  (2),  we  have 

Zm^jI-aZI.  (3) 


98 


INDUCTION  SHOCKS 


600 


400 


200 


^^^ 

Jji. 

i 


This    solved    for 

simplified 

gives 

^m  — 

M 
L 

1  +  " 

20 


40 


GO 


Fig.  1 8.  Curve  obtained  when 
the  values  of  Z  given  by  the 
application    of    the    formula 

/  to  the  experi- 


=(!-) 


ments  performed  with  a  primary- 
voltage  of  2  are  plotted  against 
the  values  of  K  used  in  these  ex- 
periments. Abscissae  represent 
values  of  K;  ordinates  represent 
values  of  Z.  The  equation  for 
this  curve  is  K  =  iS  Z. 


Zm   and 


(4) 


an  equation  which  enables 
us  to  determine  the  value 
of  make  stimuli  at  any 
given  primary  voltage,  for 
which  the  value  of  a  is 
known. 

There  remains  now  for 
the  completion  of  the  make 
shock  formula  only  the 
establishment  of  a  definite 
relationship  between  the 
values  of  a  at  various 
primary  voltages  and  the 
voltages  themselves.  To 
determine  whether  such  a 
relationship  exists  another 
curve  was  plotted,  prim- 
ary voltages  against  values 
of  a  previously  determined. 
This  curve  is  represented 
in   Fig.    19.      It   has   the 


THE   MEASUREMENT  OK   MAKE   SHOCKS 


99 


simple  equation 

in  which  C  represents  a 
constant.  Substitut- 
ing in  equation  (4)  the 
value  of  a  given  by 
equation  (5),  we  have 

M 
L 


E  =  a  'C, 


is) 


z.  = 


I     c 
I  +  E 


(6) 


■  '  I 

9.{) 

— 

10 

\ 

12 

\ 

\ 

\ 

V 

\ 

H 

"V. 

) 

r^ 

t-- 



which  is  the  general 
equation  for  make  in- 
duction shocks.  The 
value  of  C  is  fixed  Fig.  19 
for  each  inductorium. 
For  the  one  with 
which  this  equation 
was  developed,  coil 
B,  its  value  is  36. 

Comparison  of  the  General  Formulae  for  Break  and 
Make  Stimuli.  If  the  general  equation  for  break  shocks 
be  written  in  the  same  form  as  the  one  for  make  shocks 
and  the  two  placed  side  by  side,  the  simple  mathematical 
relationship  existing  between  make  and  break  stimuli 
becomes    apparent.     Written    thus,    the    break    shock 


2U 

Curve  obtained  by  plotting 
against  the  different  primary  voltages 
used  in  these  experiments  the  values  of 
a  obtained  from  curves  plotted  as  in  Fig. 
I.  The  equation  for  this  curve  is  E  X  a 
=  36.  Abscissae  represent  values  of  a; 
ordinates  represent  primar>'  voltages. 


lOO  INDUCTION  SHOCKS 


formula  is 

M 

I 

7 

Comparing  this  with  the  make  shock  formula, 

M 

^--.    C 

I^  E 

the  difference  between  them  is  seen  to  be  wholly  in  the 
denominator,  and  to  consist  of  the  addition  of  a  simple 
expression  to  the  denominator  of  the  break  shock  for- 
mula to  give  the  one  for  make  shocks.  Inasmuch  as  in- 
creasing the  denominator  of  a  fraction  diminishes  the 
value  of  the  fraction,  the  formulae  express  the  well- 
known  fact  that  make  shocks  are  weaker  than  break 
shocks  produced  under  equivalent  conditions. 

In  the  formulae  as  here  presented  the  numerators  ex- 
press the  influence  upon  the  value  of  Z  of  the  position 
of  the  secondary  coil  with  respect  to  the  primary.  The 
denominators  express  the  influence  upon  Z  of  the  in- 
tensity of  the  primary  current,  and  for  make  stimuH  the 
influence  of  its  voltage  also.     Since  the  numerator  is 

M 
the  same  in  both  formulae,  i.e.,  —  '  it  follows  that  how- 


THE  MEASUREMENT  OF   MAKE   SHOCKS  lOI 

ever  the  break  stimulus  Zj,  may  compare  with  the  make 

M 
stimulus  Z^,  changmg  the  value  of  —  by  moving  the 

secondary  coil  does  not  affect  the  relationship  between 
them.  To  illustrate,  if  we  suppose  the  break  stimulus 
to  be  twice  as  intense  as  the  make  stimulus  when  the 
secondary  coil  is  at  zero,  the  break  will  continue  to  be 
twice  as  intense  as  the  make  wherever  the  secondary 
coil  is  placed,  provided,  of  course,  that  all  other  condi- 
tions remain  constant. 

Since  the  difference  between  the  two  formulae  is  wholly 
in  their  denominators,  we  may  expect  careful  analysis 
of  these  to  yield  a  full  understanding  of  the  conditions 
upon  which  depend  the  relationships  between  make  and 
break  stimuli.  The  denominator  of  the  make  shock 
formula  will  always  be  larger  than  that  of  the  break 
formula,  but  the  amount  of  difference  between  the  two 

will  vary  greatly  according  to  the  relative  values  of- 

C 
and--     This  can  best  be  shown  by  a  concrete  case.     Let 
E 

us  first  compare  the  values  of  Z^  and  Z^  in  a  hypotheti- 
cal experiment  with  coil  B  in  which  a  primary  current  of 
0.0005  ampere  at  20  volts  is  employed.  The  expression 
for  Zt  is  M 

_z_ 

2000 


I02  INDUCTION  SHOCKS 


For  Z^  the  expression  is 
M 
L 

M 
L 

2000  +  II  ' 

200I.8 

The  difference  between  the  stimulating  intensities  of  the 
two  sorts  of  shocks  is  in  this  case  less  than  one-tenth  of 
one  per  cent.  Compare  now  the  values  of  Z^  and  Z^  when 
a  primary  current  of  0.4  ampere  at  2  volts  is  used.  The 
expression  for  Z5  is  M 

~L 

2-5 


and  for  Z^  is 

M 
L 

M 
L 

2.5 +  ¥- 

20.5 

In  this  case  the  break  shock  is  more  than  eight  times  as 
intense  as  the  make. 

The  above  illustrations  present  in  concrete  form  the 
effects  upon  the  relation  between  break  and  make  stim- 
uli of  variations  in  intensity  and  voltage  of  the  primary 
current.  These  effects  may  be  stated  in  general  thus: 
The  higher  the  voltage  of  the  primary  current  and  the  less 
its  intensity,  the  more  nearly  will  make  shocks  equal  break 
shocks:  conversely,  the  lower  the  voltage  of  the  primary 
current  and  the  greater  its  intensity,  the  more  will  break 
shocks  exceed  make  shocks. 


THE   MEASUREMENT  OF   MAKE    SHOCKS  103 

The  make  shock  formula  shows  that  make  stimuU  do 
not  vary  directly  with  the  intensity  of  the  primary 
current  as  break  stimuli  do.  Although  make  shocks 
increase  absolutely  with  every  increase  in  primary  inten- 
sity, other  conditions  remaining  uniform,  the  increase 
is  relatively  sHght  when  primary  intensities  of  consid- 
erable magnitude  are  compared.  For  example,  if  with 
coil  5  a  2  volt  primary  current  be  increased  from  0.5 
ampere  to  i.o  ampere,  the  make  stimuH  will  be  increased 
only  5  per  cent,  while  break  shocks  under  the  same  cir- 
cumstances would  be  doubled. 

This  peculiarity  of  relation  of  make  shocks  to  primary 
currents  of  high  intensity  shows  itself  very  strikingly  in 
many  experiments  in  which  minimal  muscular  contrac- 
tions are  used  as  indicators  of  stimulation  strength.  In 
the  outer  parts  of  the  field  of  the  inductorium,  where  the 

values  of -^  are  small,  primary  currents  of  high  intensity 

must  be  employed  to  give  shocks  sufficient  to  elicit 
visible  response.  I  have  often  found  when  studying 
make  shocks,  especially  with  primary  currents  of  low 
voltage,  that  as  the  secondary  coil  was  pushed  out  to  a 
point  where  primary  currents  of  o.i  or  0.2  ampere  failed 
to  elicit  response,  no  increase  of  primary  intensity  up  to 
the  limits  of  my  apparatus  would  raise  the  stimulus  to 
the  threshold.  This  frequent  failure  of  relatively  enor- 
mous primary  currents  to  give  detectable  make  stimuli 


I04  INDUCTION  SHOCKS 

was  wholly  inexplicable  until  the  development  of  the 
make  shock  formula  made  its  meaning  clear. 
Although  the  make  shock  formula 


^m     — 


M 
L 


I^  E 


presents  the  appearance  of  some  complexity,  as  a  matter 
of  fact  it  is  a  comparatively  easy  task  to  derive  the  value 
of  C,  which  is  the  only  new  constant  the  equation  re- 
quires, and  with  the  constant  once  established  the  use 
of  the  formula  is  perfectly  simple.  To  determine  how 
laborious  is  the  task  of  determining  the  value  of  C,  an 
inductorium  was  taken  which  had  been  previously  cali- 
brated for  break  shocks,  and  seven  experiments  were 
found  to  yield  sufficient  data  to  establish  conclusively 
the  value  of  the  constant. 

The  experimental  procedure  is  that  described  on  p.  95. 
The  interpretation  of  the  results  so  as  to  establish 
the  constant  depends  upon  recognition  of  the  fact  that 
in  such  experiments  as  these  the  value  of  Z^  for  the  inner 
positions  of  the  secondary  coil,  where  threshold  stimu- 
lation is  obtained  with  very  small  primary  currents,  is 
practically  independent  of  the  value  of  the  constant; 
whereas  the  value  of  Z^  for  secondary  positions  far  out 
on  the  scale,  where  heavy  primary  currents  must  be 


THE  MEASUREMENT  OF  MAKE  SHOCKS  1 05 


used,  can  be  correctly  determined  only 

if  the  constant 

is  accurately  known. 

By  transposition  of  the  equation 

M 

7           L 

I^  E 

we  obtain  the  formula  for  the  constant 

M 

C      L       I 
E     Z^      I 

(7) 

By  taking  advantage  of  the  fact  above  noted,  that 
the  value  of  Z^  for  the  inner  secondary  positions  is  inde- 
pendent of  C,  we  can  obtain  Z,^  for  any  given  experiment 

by  taking  the  product  of  —  X  /  for  these  positions. 

Since  the  value  of  Z^  is  assumed  to  be  constant  through- 
out the  experiment  we  can  apply  this  value  to  the  solu- 
tion of  equation  (7),  using  the  data  obtained  at  the  outer 

secondary  positions  to  give  —  and  -  •     From  four  expen- 

x^  1 

ments  at  2  and  4  volts  were  obtained  by  this  method  the 
following  values  of  C:  8.16,  8.0,  6.8,  9.0,  8.0,  9.8,  8.0, 
5.2,8.0.  The  average  of  these  is  7.9.  The  nearest  round 
number,  8,  was  taken  as  a  sufficiently  close  approximation 
to  the  constant,  and  was  appUed  to  three  other  experi- 


lo6  INDUCTION  SHOCKS 

ments  at  primary  voltage  ranging  from  2  to  12.  When 
so  applied,  constant  values  of  Z^  were  obtained,*  thus 
proving  the  correctness  of  the  determination. 

*  For  data  see  Martin:    Amer.  Jour,  of  Physiology,   1909,  xxiv, 
pp.  279  and  280. 


CHAPTER  XII 

ERRORS   TO   BE  AVOIDED 

Incidental  results  of  the  several  years  of  study  spent 
in  developing  the  quantitative  method  here  presented 
have  been  to  emphasize  the  importance  of  certain  pre- 
cautions, and  also  to  reveal  the  errors  committed  by 
some  users  of  induction  shocks  in  their  efforts  to  make 
quantitative  comparisons  by  indirect  methods. 

Probably  the  most  urgent  general  precaution  calling 
for  discussion  is  that  of  maintaining  good  electrical  con- 
tacts throughout.  In  a  mechanism  so  complicated  as 
that  shown  in  Fig.  8  loose  contacts  which  may  easily 
escape  observation  are  hkely  to  render  quantitative  ob- 
servations completely  valueless.  The  user  of  the  appa- 
ratus must  keep  continually  in  mind  the  importance  of 
maintaining  tight  contacts,  and  by  frequent  inspection 
must  assure  himself  that  they  are  so.  The  shding  con- 
tacts provided  for  the  secondary  coils  in  some  forms  of 
inductoria  are  very  untrustworthy  and  should  not  be 
used  if  fixed  ones  are  available. 

In  apph'ing  stimulating  electrodes  one  must  have  in 

mind  that  the  induced  current  stimulates  at  the  cathode, 

and   must   know   which   electrode   this   is.     A   simple 

107 


Io8  INDUCTION  SHOCKS 

means  of  distinguishing  the  poles  of  the  secondary  cir- 
cuit is  to  apply  them  to  a  sheet  of  filter  paper  moistened 
with  a  mixture  of  starch  paste  and  potassium  iodide 
solution.  If  a  strong  primary  current  is  made  and 
broken  rapidly,  and  the  secondary  makes  or  breaks  are 
short-circuited  each  time,  a  blue  deposit  presently  ap- 
pears at  the  anode,  indicating  the  accumulation  there 
of  iodin  ions  which  react  with  the  starch.  It  should  be 
remembered  that  make  shocks  and  break  shocks  are 
opposite  in  direction,  so  that  the  pole  which  is  revealed 
as  the  anode  for  break  shocks  is  the  cathode  for  makes. 

The  development  of  a  mathematical  expression  for  the 
influence  of  secondary  resistance  on  stimulating  value 
has  shown  the  fallacy  of  a  method  sometimes  employed 
for  varying  stimulating  strengths  quantitatively  by  in- 
cluding known  resistances  in  the  secondary  circuit  and 
assuming  that  the  strength  of  stimulus  is  reduced  in 
exact  proportion  with  the  increase  of  resistance.  As  the 
equation  (p.  76)  shows,  the  strength  of  stimulus  not 
only  does  not  vary  in  exact  proportion  with  the  resist- 
ance, but  the  relationship  actually  existing  is  not  apt  to 
be  the  same  in  two  successive  experiments,  owing  to  the 
interrelation  between  secondary  resistance  and  cathode 
surface. 

This  same  interrelation  explains  the  error  of  another 
procedure  which  has  sometimes  been  employed  for 
the  purpose  of  overcoming  inequalities  in  stimulation 


ERRORS   TO   BE   AVOIDED  109 

strength  due  to  differences  in  secondary  resistance, 
namely  the  introduction  of  a  very  high  additional  re- 
sistance into  the  secondary  circuit,  thereby  making  fluc- 
tuations in  tissue  resistance  relatively  negligible.  That 
this  device  is  perfectly  adequate  in  experiments  in  which 
a  single  tissue  of  varying  resistance  is  under  examination 
is  of  course  obvious;  there  being  under  such  circum- 
stances no  variation  in  cathode  surface.  But  in  ex- 
periments in  which  different  tissues  are  being  compared 
the  introduction  of  high  additional  resistance  into  the 
secondary  circuit  is  more  apt  to  be  misleading  than 
otherwise  because  of  the  cumulative  effect  of  variations 
in  cathode  surface.  The  point  can  best  be  illustrated 
by  a  concrete  example: 

Experiment  of  March  7,  1910.  —  Frog's  gastrocnemius  muscle  stim- 
ulated directly.  In  the  first  test  the  cathode  was  in  contact  with  the 
surface  of  the  muscle,  but  did  not  penetrate  it.  When  the  tissue  only 
was  in  the  secondary  circuit,  the  total  secondary  resistance  was  17,000 
ohms.  A  minimal  contraction  was  secured  with  a  \'alue  of  Z  equal  to 
6.6.  When  70,000  ohms'  additional  secondary  resistance  was  intro- 
duced, the  value  of  Z  was  16.8.  By  calculation  the  value  of  A  was 
found  to  be  28,000,  and  that  of  the  specific  stimulus  /3  to  be  4.1.*  In  the 
second  test  the  cathode  was  thrust  directly  through  the  muscle  tissue; 
the  secondary  resistance  was  5400  ohms;  the  value  of  Z  was  6.1.  When 
70,000  ohms'  additional  resistance  was  introduced,  the  value  of  Z  was 
40.5.  The  calculated  value  of  A  was  7000,  and  of  /3  3.45.  In  this  case 
the  values  of  Z  as  determined  with  the  tissue  only  in  the  secondary 
circuit  represent  much  more  nearly  the  true  relationships  between  the 
stimuli  than  do  the  values  as  determined  with  a  large  additional  re- 
sistance in  the  circuit.     In  reality  the  stimulus  applied  in  the  first  test 

*  For  the  equations  used  in  this  calciilation  see  p.  77. 


no  INDUCTION   SHOCKS 

was  stronger  than  in  the  second,  whereas,  if  reliance  were  placed  upon 
the  results  given  when  the  high  additional  resistance  was  in  circuit,  it 
would  appear  that  the  second  stimulus  was  more  than  twice  as  strong 
as  the  first.  The  subjoined  tabulation  will  serve  to  emphasize  the 
error: 

Z  (tissue  only)     ohL^'add^d)      ^ 

First 6.6  16.8  4.1 

Second 6.1  40.5  3.45 

Ratio  of  ist  to  2d 1.08  0.41         1. 19 

In  determining  specific  stimulation  values  by  means 

ZA 

of  the  expression  /3  =  '  particularly   when    the 

tissues  stimulated  have  high  resistances,  errors  in  de- 
termining the  value  of  A  may  easily  vitiate  the  results. 
It  will  usually  be  found  desirable  to  determine  values  of 
Z  for  at  least  three  secondary  resistances  in  addition  to 
the  tissue  resistance  itself.  If  the  values  of  Z  thus 
obtained  are  plotted  against  their  respective  resistances 
the  curve  which  they  yield  reveals  at  once  whether 
errors  have  been  made  in  the  determinations.  The 
curve  should  be  a  straight  line,  cutting  the  ordinate  for 
zero  resistance  at  some  point  above  the  base  line.  Minor 
errors  may  be  allowed  for  by  drawing  the  curve  to  make 
them  balance  one  another.  This  precaution  is  unnec- 
essary when  tissues  of  low  resistance  are  studied,  since 
with  them  small  errors  in  determining  A  are  less  sig- 
nificant. 
These  are  among  the  less  obvious  sources  of  error  in 


ERRORS   TO   BE  AVOIDED  III 

quantitative  work,  and  are  therefore  discussed  here. 
The  more  apparent  ones  need  not  be  mentioned,  since 
they  are  sure  to  suggest  themselves  to  any  user  of  the 
method  here  presented. 

In  the  use  of  this  quantitative  method,  as  in  most 
procedures  involving  numerous  factors,  a  technic^ue, 
which  seems  at  the  outset  highly  complicated,  becomes 
with  practice  easy  to  carry  out.  Its  inclusion  as  part 
of  the  experimental  routine  of  the  working  physiologist 
is  therefore  justified.  To  facilitate  such  inclusion  is 
the  purpose  of  this  manual. 


INDEX 

Ammeter,  use  of,  24. 

shunt  for,  24. 

du  Bois  Reymond  inductorium,  3. 
Break  induced  currents,  7. 
Break  shocks,  course  of,  32. 

equation  for,  35,  60. 

Calibration  of  inductorium,  apparatus  required  for,  23. 
for  break  shocks,  55. 
in  region  of  iron  core,  58. 
Cathode,  method  of  determining,  107. 
Circuit,  primar}',  make  and  break  of,  60. 

variables  concerned  in,  13. 
variations  in  break  of,  60. 
variations  in  make  of,  61. 
secondarj',  variables  concerned  in,  13. 
Coil,  secondary',  effect  of  position  of  on  strength  of  shock,  7,  13,  15. 
Core,  iron,  correction  for  magnetization  of,  46. 

effects  of  on  stimulation  strengths,  43. 
in  critical  region,  47. 
magnetization  of,  43. 
Current  density,  importance  of,  76. 
extra,  10. 
induced,  5. 

direction  and  intensity  of,  5. 
method  of  varj'ing,  7. 
sources  of  variation  in,  13. 
primar>',  adjustment  of,  25. 
measurement  of,  24. 
voltage,  relation  of  to  make  stimuli,  97. 
113 


114  INDEX 

Density  of  current,  importance  of,  76. 

Edelmann  method  of  measuring  induction  shocks,  20. 
Electrodynamometer  of  Hoorweg-Giltay,  21. 
Electrode  contacts,  effect  of  on  strength  of  shocks,  13,  76. 
Electrodes,  needle,  27. 

Sherrington,  27. 
Extra  current,  10. 

Faradimeter  of  Edelmann,  20. 

Fick-Meyer  method  of  measuring  induction  shocks,  15. 

V.  Fleischl  method  of  measuring  induction  shocks,  18. 

application  of,  to  calibration,  56. 
Force,  lines  of,  5. 

Galvanometer,  ballistic,  26. 

Hoorweg-Giltay  method  of  measuring  induction  shocks,  21. 

Induced  current,  direction  and  intensity  of,  5. 
form  of,  8. 
break,  comrse  of,  32. 
make  and  break,  7. 
measurement  of,  historical,  14. 
method  of  varying,  7. 
sources  of  variation  in,  13. 
Inductance,  8. 

of  secondary  coil,  34. 
determination  of,  50. 
equation  for,  53. 
Induction,  discovery  of,  2. 
mutual,  34. 

determination  of,  38. 
relation  of  to  calibration,  36. 
Induction  coil,  standard,  for  use  in  calibration,  26. 

structure  of,  3. 
Induction  shocks,  apparatus  for  quantitative  use  of,  30. 
break,  course  of,  32. 


INDEX  '  115 

Induction  shocks,  break,  equation  for,  35. 

comparison  of  make  and  break,  102. 
make,  measurement  of,  94. 

equation  for,  99. 
measurement  of  historical,  14. 

Edelmann  method,  20. 
V.  FleischI  method,  18. 
Hoorweg-Giltay  method,  21. 
Kronecker  method,  16. 
Meyer-Fick  method,  15. 
Pfliiger  method,  14. 
Wertheim-Salomonson  method, 
18. 
sources  of  variation  in,  13. 
stimulate  at  cathode,  72,  107. 
Inductorium,  du  Bois  Reyraond  type,  3. 
principle  of,  4. 

calibration  of,  apparatus  required,  23. 
procedure,  28. 
for  break  shocks,  55. 
for  make  shocks,  94. 
in  region  of  iron  core,  58. 
"standard,"  23,  88. 
Berlin  standard,  88. 

shortcomings  of,  92. 
structure  of,  3. 

effect  of  on  strength  of  shock,  13. 
relation  to  determination  of  specific  stim- 
ulus, 78. 
Iron  core,  effect  of  on  strength  of  shock,  13,  43. 

in  critical  region,  47. 
magnetization  of,  43. 

correction  for,  46. 

Key,  automatic,  necessity  for,  61. 
knife-blade,  construction  of,  63. 

advantages  of,  64,  67,  70. 
operating  device  for,  65. 


Il6  INDEX 

Key,  knife-blade,  short-circuiting  device  for,  67. 

make  and  break,  essentials  of,  62. 
Kronecker  method  of  measuring  induction  shocks,  16. 

Magnetization  of  core,  correction  for,  46. 
Make  induced  currents,  7. 

shocks,  equation  for,  99. 

measurement  of,  94. 

constant,  determination  of,  104. 
Meyer-Fick  method  of  measuring  induction  shocks,  15. 

Pfliiger  method  of  measuring  induction  shocks,  14. 
Primary  circuit,  make  and  break  of,  60. 

variables  concerned  in,  13. 
variations  in  break  of,  60. 
in  make  of,  61. 
current,  adjustment  of,  25. 
measiurement  of,  24. 
relation  of  to  strength  of  shock,  13. 
voltage,  relation  of  to  make  stimuli,  97. 

Resistance  of  tissue,  apparatus  for  measuring,  26. 
determination  of,  72. 
effect  of  on  strength  of  shock,  13,  73. 
relation  of  to  secondary  resistance,  71. 

Secondary  circuit,  variables  concerned  in,  13. 
Shocks,  induction,  sources  of  variation  in,  13. 

comparison  of  make  and  break,  102. 
break,  course  of,  32. 

equation  for,  35,  60. 
make,  form  of,  8. 

equation  for,  99. 

determination  of  constant  for,  104. 
Short-circuiting  device  for  knife-blade  key,  67. 
Shunt  for  ammeter,  24. 

Specific  stimuli,  precautions  necessary  in  obtaining,  no. 
Stimuli,  faradic,  historical,  14. 


INDEX  117 

Stimulus,  actual,  equation  for,  76. 

precautions  necessary  in  obtaining,  no. 
when  not  essential,  80. 

Tissue  resistance,  apparatus  for  measuring,  26. 
determination  of,  72. 
effect  of,  on  strength  of  stimulus,  13,  73. 
importance  of,  21. 
relation  of  to  entire  resistance,  71. 

Voltage  of  primary  current,  relation  of  to  make  stimuli,  97. 

Wertheim-Salomonson  method  of  measuring  induction  shocks,  t^^ 


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Ulke's  Modem  Electrolytic  Copper  Refining 8vo,     3  00 

West's  American  Foundry  Practice 12mo.     2  50 

Moulders'  Text  Book 12mo.     2  50 


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*  Browning's  Introduction  to  the  Rarer  Elements 8vo. 

Brush's  Manual  of  Determinative  Mineralogy.     (Penfield.) 8vo, 

Butler's  Pocket  Hand-book  of  Minerals 16mo,  mor. 

Chester's  Catalogue  of  Minerals 8vo,  paper. 

Cloth. 

*  Crane's"Gold  and  Silver 8vo. 

Dana's  First  Appendix  to  Dana's  New  "System  of  Mineralogy".  .Large  8vo, 
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Douglas's  Untechnical  Addresses  on  Technical  Subjects 12mo, 

•  Eakle's  Mineral  Tables 8vo, 

*  Eckel's  Building  Stones  and  Clays Svo. 

Goesel's  Minerals  and  Metals:  A  Reference  Book 16mo,  mor. 

*  Groth's  The  Optical  Properties  of  Crystals.     (Jackson.) Svo, 

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*  Hayes's  Handbook  for  Field  Geologists 16mo,  mor. 

Iddings's  Igneous  Rocks 8vo, 

Rock  Minerals .  Svo, 

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Johannsea's  Determination  of  Rock-forming  Minerals  in  Thin  Sections.  8vo, 

With  Thumb  Index  $5  00 

*  Martin's  Laboratory    Guide    to    Qualitative    Analysis    with    the    Blow- 

pipe  c 12mo,  0  60 

Merrill's  Non-metallic  Minerals:  Their  Occurrence  and  Uses 8vo,  4  00 

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